Inscribe a hexagon in a unit circle such that AB = CD = EF = 1.
Now the midpoints of BC, DE, and FA form an equilateral triangle.
See A Better Nature.
Author: Greg Ross
Saying Nothing
In a historic passage Mallarmé describes the terror, the sense of sterility, that the poet experiences when he sits down to his desk, confronts the sheet of paper on which his poem is supposed to be composed, and no words come to him. But we might ask, why could not Mallarmé, after an interval of time, have simply got up from his chair and produced the blank sheet of paper as the poem that he sat down to write? Indeed, in support of this, could one imagine anything that was more expressive of, or would be held to exhibit more precisely the poet’s feelings of inner devastation than the virginal paper?
— Richard Wollheim, “Minimal Art,” in Minimal Art, ed. Gregory Battcock, 1968
Rolling
Arthur W.J.G. Ord-Hume calls this “the most graceful and simple perpetual motion machine of all time.” It was offered by American inventor F.G. Woodward in the 19th century. A heavy wheel is mounted between two rollers so that the wheel’s weight causes it to roll continuously in the direction of the arrow.
Or so Woodward hoped. Ord-Hume notes that the principle required the left half of the wheel always to be heavier than the right half. “Sadly, it wasn’t.”
Ground Zero
There is at Columbia University’s Arden House Conference Center a statue of a cat in bronze. It stands on a floor at the head of a stairway that leads into a common room at a lower level. Presumably it is of some value, or believed to be … inasmuch as the managers have chained it to the railing — to forestall theft, I suppose, as if it were a television set in a squalid motel. Such might be the obvious interpretation. But I am open to the suggestion that it is not a chained sculpture of a cat but a sculpture of a chained cat, one end of which is wittily attached to a piece of reality. … Of course what we take to be a bit of reality can in fact be part of the work, which is now a sculpture of a cat-chained-to-an-iron-railing, though the moment we allow it to be a part of the work, where does or can the work end? It becomes a kind of metaphysical sandpit, swallowing the universe down into itself.
— Arthur Danto, The Transfiguration of the Commonplace, 1981
Skin Deep
During the filming of Planet of the Apes in 1967, Charlton Heston noted “an instinctive segregation on the set. Not only would the apes eat together, but the chimpanzees ate with the chimpanzees, the gorillas ate with the gorillas, the orangutans ate with the orangutans, and the humans would eat off by themselves. It was quite spooky.”
James Franciscus noticed the same thing filming Beneath the Planet of the Apes in 1969. “During lunch I looked up and realized, ‘My God, here is the universe,’ because at one table were all the orangutans eating, at another table were the apes, and at another table were the humans. The orangutan characters would not eat or mix with the ape characters, and the humans wouldn’t sit down and eat with any one of them.
“I remember saying, ‘Look around — do you realize what’s happening here? This is a little isolated microcosm of probably what’s bugging the whole world. Call it prejudice or whatever you want to call it. Whatever’s different is to be shunned or it’s frightening or so forth.’ Nobody was intermingling, even though they were all humans underneath the masks. The masks were enough to bring out our own little genetic natures of fear and prejudice. It was startling.”
(From Joe Russo and Larry Landsman, Planet of the Apes Revisited, 2001.)
Black and White
The Froggy Problem
Speaking of Lewis Carroll — and further to Wednesday’s logic exercise — here’s the king of all Carroll’s logic problems. What’s the strongest conclusion that can be drawn from these premises?
- When the day is fine, I tell Froggy “You’re quite the dandy, old chap!”
- Whenever I let Froggy forget that 10 pounds he owes me, and he begins to strut about like a peacock, his mother declares “He shall not go out a-wooing!”
- Now that Froggy’s hair is out of curl, he has put away his gorgeous waistcoat.
- Whenever I go out on the roof to enjoy a quiet cigar, I’m sure to discover that my purse is empty.
- When my tailor calls with his little bill, and I remind Froggy of that 10 pounds he owes me, he does not grin like a hyena.
- When it is very hot, the thermometer is high.
- When the day is fine, and I’m not in the humor for a cigar, and Froggy is grinning like a hyena, I never venture to hint that he’s quite the dandy.
- When my tailor calls with his little bill and finds me with an empty pocket, I remind Froggy of that 10 pounds he owes me.
- My railway shares are going up like anything!
- When my purse is empty, and when, noticing that Froggy has got his gorgeous waistcoat on, I venture to remind him of that 10 pounds he owes me, things are apt to get rather warm.
- Now that it looks like rain, and Froggy is grinning like a hyena, I can do without my cigar.
- When the thermometer is high, you need not trouble yourself to take an umbrella.
- When Froggy has his gorgeous waistcoat on, but is not strutting about like a peacock, I betake myself to a quiet cigar.
- When I tell Froggy that he’s quite a dandy, he grins like a hyena.
- When my purse is tolerably full, and Froggy’s hair is one mass of curls, and when he is not strutting about like a peacock, I go out on the roof.
- When my railways shares are going up, and when it’s chilly and looks like rain, I have a quiet cigar.
- When Froggy’s mother lets him go a-wooing, he seems nearly mad with joy, and puts on a waistcoat that is gorgeous beyond words.
- When it is going to rain, and I am having a quiet cigar, and Froggy is not intending to go a-wooing, you had better take an umbrella.
- When my railway shares are going up, and Froggy seems nearly mad with joy, that is the time my tailor always chooses for calling with his little bill.
- When the day is cool and the thermometer low, and I say nothing to Froggy about his being quite the dandy, and there’s not the ghost of a grin on his face, I haven’t the heart for my cigar!
Unfortunately, Carroll died before he was able to publish the solution — but he warned that it contains “a beautiful ‘trap.'”
Author!
How do I know that I’m not just a fictional character in some imagined story? What could I learn about myself that would prove that I’m real? “I am human, male, brunette, etc., but none of that helps,” writes UCLA philosopher Terence Parsons. “I see people, talk to them, etc., but so did Sherlock Holmes.”
Descartes would say that the very fact that I’m thinking about this shows that I exist: cogito ergo sum. But a fictional character could make the same argument. “Hamlet did think a great many things,” writes Jaakko Hintikka. “Does it follow that he existed?” Robert Nozick adds, “Could not any proof be written into a work of fiction and be presented by one of the characters, perhaps one named ‘Descartes’?”
Tweedledee tells Alice that she’s only a figment of the Red King’s dream. “If that there King was to wake,” adds Tweedledum, “you’d go out — bang! — just like a candle!”
Alice says, “Hush! You’ll be waking him, I’m afraid, if you make so much noise.”
“Well, it’s no use YOUR talking about waking him,” replies Tweedledum, “when you’re only one of the things in his dream. You know very well you’re not real.”
“It seems to me that this is a philosophical problem that deserves to be treated seriously on a par with issues like the reality of the external world and the existence of other minds,” Parsons writes. “I don’t know how to solve it.”
(Terence Parsons, Nonexistent Objects, 1980; Charles Crittenden, Unreality, 1991; Robert Nozick, “Fiction,” Ploughshares 6:3 [1980], 74-78; Jaakko Hintikka, “Cogito, Ergo Sum: Inference or Performance?”, Philosophical Review 71:1 [January 1962], 3-32.)
In a Word
theic
n. one addicted to immoderate tea-drinking
Scattered Objects
If a flock of birds disperses gradually, at what point does it cease to be a flock?
“There is at the moment a pipe on my desk,” wrote MIT philosopher Richard Cartwright in 1987. “Its stem has been removed, but it remains a pipe for all that; otherwise no pipe could survive a thorough cleaning.”
But he also owned a two-volume set of John McTaggart’s The Nature of Existence, one volume of which was in Cambridge and the other in Boston. Do those two volumes still make one thing? If so, is there a “thing” composed of the Eiffel Tower and the Old North Church? Why not?
(From Cartwright’s Philosophical Essays.)