Swiss chemist Hans Heinrich Landolt discovered this startling reaction in 1886: Two colorless solutions are mixed and, after a distinct delay, the liquid turns dark blue due to the formation of a triiodide–starch complex. It’s called the iodine clock reaction.
Cistercian Numerals
In the 13th century, Cistercian monks worked out a system of numerals in which a single glyph can represent any integer from 1 to 9,999:
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Once you’ve mastered the digits in the top row, you can represent tens by flipping them (second row), hundreds by inverting them (third row), and thousands by doing both (fourth row). And now you can combine these symbols to produce any number under 10,000:
The monks eventually dropped the system in favor of Arabic numerals, which reached northwestern Europe at about the same time, but it was being used informally elsewhere as recently as the early 20th century.
To Have and to Hold
The brank consisted of a kind of crown or framework of iron, which was locked upon the head of the delinquent. It was armed in front with a gag, plate, point or knife of the same metal, which was fitted in such a manner as to be inserted in the scold’s mouth so as to prevent her moving her tongue; or, more cruel still, it was so placed that if she did move it, or attempt to speak, her tongue was cruelly lacerated, and her sufferings intensified. With this cage upon her head, and with the gag pressed and locked upon the tongue, the poor creature was paraded through the streets, led by the beadle or constable, or else she was chained to the pillory or market cross to be the object of scorn and derision, and to be subjected to all the insults and degradations that local loungers could invent.
— “Muzzles for Ladies,” Strand, November 1894
Aviculture
A logic exercise by Lewis Carroll: What conclusion can be drawn from these premises?
- No birds, except ostriches, are 9 feet high.
- There are no birds in this aviary that belong to anyone but me.
- No ostrich lives on mince pies.
- I have no birds less than 9 feet high.
Unquote
“Landscape painting is the obvious resource of misanthropy.” — William Hazlitt
Three by Three
From Lee Sallows:
(Thanks, Lee!)
Mnemonic
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.
Limerick
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
Maverick
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.)
Front Matter
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?