One more example of the trials of 19th-century house servants — in 1832 Elizabeth Fox, Baroness Holland, strained a sinew in her back:
Lady Hardy … said to her hostess after dinner, in the presence of the gentlemen, ‘Is it very painful? Where is it?’ Upon which her Ladyship called her page, made him turn his back to her, put her finger on his posterior regions, and said, ‘Here, Lady Hardy.’
(From Giles Fox-Strangways’ 1937 Chronicles of Holland House, 1820-1900.)
These are called Borwein integrals, after David and Jonathan Borwein, the father-and-son mathematicians who first presented them in 2001.
Engineer Hanspeter Schmid writes, “[W]hen this fact was recently verified by a researcher using a computer algebra package, he concluded that there must be a ‘bug’ in the software. It is not a bug, though; this series of integrals really only results in π/2 up to a certain point, and then breaks down. This astonishes most mathematically educated readers, as especially those readers mentally extrapolate the sequence shown above and find it surprising that something fundamental should change when the factor sinc(x/15) is introduced.” He gives a graphic explanation of what’s happening.
(David Borwein and Jonathan M. Borwein, “Some Remarkable Properties of Sinc and Related Integrals,” Ramanujan Journal 5:1 [March 2001], 73–89.) (Thanks, Dan.)
When Virginia senator William B. Spong Jr. first went to Washington, he worried that the media might mistakenly pronounce his name Sponge.
But he observed that his Senate colleagues included Russell B. Long (D-La.) and Hiram L. Fong (R-Hawaii).
So in introducing himself at the National Press Club, he announced that the three of them would be introducing a bill to protect the rights of songwriters in Hong Kong. It would be called the Long Fong Spong Hong Kong Song Bill.
They never introduced the bill, but the media never mispronounced Spong’s name.
During World War I the Red Cross solicited contributions by literally sucking them out of a crowd with a vacuum cleaner.
The stunt took place on May 25, 1917, before the New York Public Library. From Scientific American: “While a soldier and a sailor urged the public to hand in their contributions the suction tube of the machine was reached out over the crowd. The suction was sufficient to draw up pieces of money of any denomination and deposit them in the bag of the vacuum cleaner. By this means it was possible to reach the crowd readily and it was unnecessary for a contributor to elbow his way through the jam in order to reach the Red Cross workers.”
The National Archives notes, “So great was the eagerness of the people to have their coins taken in by the cleaner that the bag inside the vacuum cleaner had to be emptied several times.”
This passage is from Rudyard Kipling’s 1910 story “Brother Square-Toes.” What’s notable about the bolded section?
‘I’ll have to bide ashore and grow cabbages for a while, after I’ve run this cargo; but I do wish’ — Dad says, going over the lugger’s side with our New Year presents under his arm and young L’Estrange holding up the lantern — ‘I just do wish that those folk which made war so easy had to run one cargo a month all this winter. It ‘ud show ’em what honest work means.’
‘Well, I’ve warned ye,’ says Uncle Aurette. ‘I’ll be slipping off now before your Revenue cutter comes. Give my love to sister and take care o’ the kegs. It’s thicking to southward.’
In his 2008 book Impossible?, Julian Havil presents an argument offered in Massachusetts in 1854 contending that foreigners were more likely to be insane than native-born Americans. These figures were offered:
| Whole Population | |||
| Insane | Not Insane | Totals | |
| Foreign-Born | 625 | 229375 | 230000 |
| Native-Born | 2007 | 892669 | 894676 |
| Totals | 2632 | 1122044 | 1124676 |
The probability that a foreign-born person was deemed insane was 625/230000 = 2.7 × 10-3, and for a native-born person the probability was 2007/894676 = 2.2 × 10-3, which seems to support the claim.
But we get a different story when we divide the data by social hierarchy, into what were called the pauper and independent classes:
| Pauper Class | |||
| Insane | Not Insane | Totals | |
| Foreign-Born | 182 | 9090 | 9272 |
| Native-Born | 250 | 12513 | 12763 |
| Totals | 432 | 21603 | 22035 |
| Independent Class | |||
| Insane | Not Insane | Totals | |
| Foreign-Born | 443 | 220285 | 220728 |
| Native-Born | 1757 | 880156 | 881913 |
| Totals | 2200 | 1100441 | 1102641 |
In the pauper class the probability of a foreign-born person being deemed insane is 182/9272 = 0.02, which is the same as that for a native-born person (250/12763 = 0.02). And the same is true in the independent class, where both probabilities are 2.0 × 10-3. Havil writes, “So, if an adjustment is made for the status of the individuals we see that there is no relationship at all between sanity and origin” (an example of Simpson’s paradox).
“While there is a chance of the world getting through its troubles, I hold that a reasonable man has to behave as though he was sure of it. If at the end your cheerfulness is not justified, at any rate you will have been cheerful.” — H.G. Wells
Between the 1880s and the 1960s, the flag of the Turks and Caicos Islands featured an igloo. When Britain decided that the colony needed its own flag, it commissioned an artist to paint a suitable local scene. At the time, the salt industry dominated the local economy, so he sketched a man working on a quay between two piles of salt. When this was sent to London, the Admiralty artist apparently mistook these for ice, not knowing that the Turks and Caicos lie southeast of the Bahamas, and he helpfully added a door to the right pile.
Amazingly, the error remained in place until 1966, when it was discreetly removed before a state visit by Queen Elizabeth.
(Thanks, Charles.)
“Squaring the square” refers to tiling a square with other squares, each with sides of integer length.
In a “perfect” squared square, like the one above, each smaller square is of a different size. The Cambridge University team that first sought perfect squares found a novel way to go about it — they transformed the square tiling into an electrical circuit in which each square is a resistor that connects to its neighbors above and below, and then applied Kirchhoff’s circuit laws to that circuit.
The example below isn’t perfect, but the technique did succeed — the smallest perfect square they found is 69 units on a side.
(Rowland Leonard Brooks, et al., “The Dissection of Rectangles into Squares,” Duke Mathematical Journal 7:1 [1940], 312-340.)
polyhistor
n. a person of great and varied learning
suresby
n. one who may be depended upon
logomachy
n. a dispute about or concerning words
vilipend
v. to speak of with disparagement or contempt
In 1746 Samuel Johnson set out to write a dictionary of the English language. He proposed to finish it in three years.
Dr. Adams found him one day busy at his Dictionary, when the following dialogue ensued.
ADAMS. This is a great work, Sir. How are you to get all the etymologies? JOHNSON. Why, Sir, here is a shelf with Junius, and Skinner, and others; and there is a Welch gentleman who has published a collection of Welch proverbs, who will help me with the Welch. ADAMS. But, Sir, how can you do this in three years? JOHNSON. Sir, I have no doubt that I can do it in three years. ADAMS. But the French Academy, which consists of forty members, took forty years to compile their Dictionary. JOHNSON. Sir, thus it is. This is the proportion. Let me see: forty times forty is sixteen hundred. As three to sixteen hundred, so is the proportion of an Englishman to a Frenchman.
(From Boswell.) (In the end it took him seven years.)
