A logic exercise by Lewis Carroll: What conclusion can be drawn from these premises?
“Landscape painting is the obvious resource of misanthropy.” — William Hazlitt
From Lee Sallows:
(Thanks, Lee!)
English history 1066-1154 as depicted by Mark Twain:
He had discovered that taking notes using pictures helped to fix details in his memory, and in an 1899 essay he recommended the practice to children. An explanation of the diagram, starting at the bottom:
21 whales heading west: These represent William I, whose reign lasted 21 years (1066-1087). “We choose the whale for several reasons: its name and William’s begin with the same letter; it is the biggest fish that swims, and William is the most conspicuous figure in English history in the way of a landmark; finally, a whale is about the easiest thing to draw.”
13 whales heading east: William II, 1087-1100. The change in direction marks a change in leaders. “Make him spout his water forward instead of backward; also make him small, and stick a harpoon in him and give him that sick look in the eye. Otherwise you might seem to be continuing the other William, and that would be confusing and a damage.”
35 hens going west: Henry I, 1100-1135. “That is a hen, and suggests Henry by furnishing the first syllable.”
19 steers going east: Stephen of Blois, 1135-1154. “That is a steer. The sound suggests the beginning of Stephen’s name. I choose it for that reason. I can make a better steer than that when I am not excited. But this one will do. It is a good-enough steer for history.”
The essay was published in Harper’s Monthly Magazine in December 1914, four years after Twain’s death.
A performative poet of Hibernia
Rhymed himself into a hernia.
He became quite adept
At this practice, except
For the occasional non-sequitur.
— Tom Stoppard
The ancient Chinese philosopher Gongsun Long appeared to claim that a white horse is not a horse:
Is ‘a white horse is not horse’ assertible?
Advocate: It is.
Objector: How?
Advocate: ‘Horse’ is that by means of which one names the shape. ‘White’ is that by means of which one names the color. What names the color is not what names the shape. Hence, one may say ‘white horse is not horse.’
Objector: If there are white horses, one cannot say that there are no horses. If one cannot say that there are no horses, doesn’t that mean that there are horses? For there to be white horses is for there to be horses. How could it be that the white ones are not horses?
Advocate: If one wants horses, that extends to yellow or black horses. But if one wants white horses, that does not extend to yellow or black horses. Suppose that white horses were horses. Then what one wants [in the two cases] would be the same. If what one wants were the same, then ‘white’ would not differ from ‘horse.’ If what one wants does not differ, then how is it that yellow or black horses are acceptable in one case and unacceptable in the other case? It is clear that acceptable and unacceptable are mutually contrary. Hence, yellow and black horses are the same, one can respond that there are horses, but one cannot respond that there are white horses. Thus, it is evident that white horses are not horses.
Interpretations vary; one explanation is that the conundrum blurs the distinction between identity and class, exploiting an ambiguity in the Chinese language — certainly the expressions “white horse” and “horse” do not have identical meanings, but one can refer to a subset of the other.
Whether the philosopher was serious isn’t clear. His other paradoxes include “When no thing is not the pointed-out, to point out is not to point out” and “There is no 1 in 2.”
More trouble with horse color.
03/08/2024 UPDATE: A Swedish Facebook meme of 2012: Horses are a fruit that does not exist. (Thanks, Mikael.)
David B. Lewis’ 1983 book Eureka!: Math Fun From Many Angles begins with this notice:
Errata
1. There are no mistakes in this book. The above should read ‘Erratum.’
Is the correction a mistake or not?
In 1819, as the Bank of England struggled against counterfeiters, T.C. Hansard proposed a note that combined such a variety of typefaces that a lone forger couldn’t hope to duplicate it — the faces descended all the way to Diamond, the smallest available, and the bottom of each note would be filled with 140 lines of fine print containing hidden “private marks,” such as individual letters printed in italic or small capitals.
To create even the authentic version would have required a team of 20 people, from punchcutters to engine makers, to fulfill the typographical and other design flourishes. Hansard estimated that producing the first note would have cost as much as £2,000 and taken up to a year, “but after that the production will be so rapid, that with the labour of four Men only, without the assistance of any Steam Machinery, 40,000 Notes may be produced in a Day of the finest Workmanship, at the Expense, including Paper, of Half a Farthing each Note.”
In the end the proposal wasn’t adopted — small notes were withdrawn from circulation in 1821, and the search was dropped.
(Virginia Hewitt, “Beware of Imitations: The Campaign for a New Bank of England Note, 1797-1821,” Numismatic Chronicle 158 [1998], 197-222.)
During the middle ages there existed a monastery, in which lived twenty-four monks, presided over by a blind abbot. The cells of the monastery were planned as shown in the accompanying figure, passages being arranged along two sides of each of the outer cells and all round the inner cell, in which the abbot took up his quarters. Three monks were allotted to each cell, making, of course, nine monks in each row of cells. The abbot, being lazy as well as blind, was very remiss in making his rounds, but provided he could count nine heads on each side of the monastery he retired into his own cloister, contented and satisfied that the monks were all within the building, and that no outsiders were keeping them company. The monks, however, taking advantage of their abbot’s blindness and remissness, conspired to deceive him, a portion of their number sometimes going out and at other times receiving friends in their cells. They accomplished their deception, and it never happened that strangers were admitted when monks were out, yet there never were more nor less than nine persons upon each side of the building. Their first deception consisted in four of their number going out, upon which four monks took possession of each of the cells numbered 1, 3, 6, and 8, one monk only being left in each of the other cells; nine monks being thus on each side of the building. Upon returning, the four monks brought in four friends, when it was necessary to arrange the twenty-eight persons, two in each of the cells 1, 3, 6, and 8, and five in each of the others; still nine heads only were to be counted in either row. Emboldened by success, eight outsiders were introduced, and the thirty-two persons now were arranged, one only in each of the cells 1, 3, 6, and 8, but seven in each of the other cells; again, according to the abbot’s system of counting, all was well. In the next endeavour, the strangers all went away and took six monks with them, leaving but eighteen at home to represent twenty-four; these eighteen placed themselves five in each of the cells 1 and 8 and four in each of the cells 3 and 6; the remaining cells were empty, but the cells on each side of the building still contained nine monks. On returning, the six truants each brought two friends to pass the night, and the thirty-six retired to rest, nine in each of the cells 2, 4, 5, and 7; the remainder were empty, and the abbot was quite satisfied that the monks were alone in the monastery.
— Cassell’s Book of In-Door Amusements, Card Games and Fireside Fun, 1882
I loved thee, beautiful and kind,
And plighted an eternal vow;
So alter’d are thy face and mind,
‘Twere perjury to love thee now.
— Robert, Earl Nugent (1709-1788)