A problem from the Leningrad Mathematical Olympiad: You have 32 stones, each of a different weight. How can you find the two heaviest in 35 weighings with an equal-arm balance?
“Men are apt to mistake the strength of their feeling for the strength of their argument. The heated mind resents the chill touch and relentless scrutiny of logic.” — William Gladstone
“The knowledge of the theory of logic has no tendency whatever to make men good reasoners.” — Thomas Macaulay
Italian artist Salvatore Garau has auctioned an invisible sculpture titled Io Sono (“I am”) for 15,000 euros. The buyer receives a certificate of authentication and agrees to display the nonexistent artwork in a private home in an unobstructed area 5 feet square.
Last month the artist displayed another immaterial sculpture, Buddha in Contemplation, near the entrance to the Gallerie d’Italia in Milan. The area of its location was marked off with tape.
Garau said that the titles of his works “activate” viewers’ imagination. “When I decide to ‘exhibit’ an immaterial sculpture in a given space, that space will concentrate a certain amount and density of thoughts at a precise point, creating a sculpture that, from my title, will only take the most varied forms. After all, don’t we shape a God we’ve never seen?”
I was in a house I did not know, which had two storeys. It was ‘my house.’ I found myself in the upper storey, where there was a kind of salon furnished with fine old pieces in Rococo style. On the walls hung a number of precious old paintings. I wondered that this should be my house and thought ‘not bad.’ But then it occurred to me that I did not know what the lower floor looked like. Descending the stairs, I reached the ground floor. There everything was much older. I realised that this part of the house must date from about the fifteenth or sixteenth century. The furnishings were mediaeval, the floors were of red brick. Everywhere it was rather dark. I went from one room to another thinking ‘now I really must explore the whole house.’ I came upon a heavy door and opened it. Beyond it, I discovered a stone stairway that led down into a cellar. Descending again, I found myself in a beautifully vaulted room which looked exceedingly ancient. Examining the walls, I discovered layers of brick among the ordinary stone blocks, and chips of brick in the mortar. As soon as I saw this, I knew that the walls dated from Roman times. My interest by now was intense. I looked more closely at the floor. It was of stone slabs and in one of these I discovered a ring. When I pulled it, the stone slab lifted and again I saw a stairway of narrow stone steps leading down to the depths. These, too, I descended and entered a low cave cut into rock. Thick dust lay on the floor and in the dust were scattered bones and broken pottery, like remains of a primitive culture. I discovered two human skulls, obviously very old, and half disintegrated. Then I awoke.
Carl Jung had this dream in 1909, during a voyage to America with Freud. He took it to be an image of his psyche … but it also bears a striking resemblance to H.P. Lovecraft’s 1924 short story “The Rats in the Walls.”
Sometime in the late 5th century, a brutal mass killing took place at the settlement known as Sandby Borg on the Swedish island of Öland. It appears that the residents had just enough warning of the attack to hide their valuables. After the slaughter, the bodies left where they lay, the houses closed up, and the area abandoned and apparently taboo for years.
That makes it a valuable portrait of daily life in Scandinavia. “It’s compelling because people were killed inside the houses, and then the killers went out, locked the doors, and left,” said Swedish archaeologist Ulf Näsman. The attackers left even the livestock behind.
The reason for the attack is still a mystery. The usual signs of a battle or siege are missing — in fact the remains of the victims are oddly bare. “There is no dress, such as belt buckles [on the skeletons],” Näsman says. “Were they caught unawares at night? Maybe they were nude or in night dress and taken by surprise.”
And, strangely, two of the victims were found with sheep or goat teeth in their mouths. “It wasn’t enough to kill them and leave them in their houses,” says archaeologist Helena Victor, who directs the excavation. “It’s really, really ugly treatment.”
A bizarre detail from Thomas Southcliffe Ashton and Joseph Sykes’ 1964 book The Coal Industry of the Eighteenth Century:
British miners often had to work in near-total darkness, as any flame might ignite methane gas.
So, in the more explosion-prone mines, “colliers sometimes tried to carry on their work by the feeble light of phosophorous and putrescent fish.”
Armenian pianist Tigran Hamasyan writes music of densely sophisticated rhythmic complexity, arranging subdivisions of grouped tuplets over a ground pulse that’s sometimes withheld, leading the ear into assumptions that are later revealed to be mistaken. Below, composer David Bruce analyzes some of his work.
In the spirit of amity, Vilnius, Lithuania, has installed a “portal” that allows residents to make contact in real time with the inhabitants of Lublin, Poland. Each city hosts a large circular screen and cameras by which residents can interact in real time via the Internet.
“Humanity is facing many potentially deadly challenges; be it social polarisation, climate change or economic issues,” said organizer Benediktas Gylys. “However, if we look closely, it’s not a lack of brilliant scientists, activists, leaders, knowledge or technology causing these challenges. It’s tribalism, a lack of empathy and a narrow perception of the world, which is often limited to our national borders. That’s why we’ve decided to bring the PORTAL idea to life — it’s a bridge that unifies and an invitation to rise above prejudices and disagreements that belong to the past. It’s an invitation to rise above the us and them illusion.”
The planners hope to install dozens of similar portals around the world. “Meaningful projects like this one are born when diverse people succeed in working together and achieving synchronicity,” said Adas Meskenas, director of LinkMenu fabrikas, which built the portal. “And this is just another example of what people who are united can do.”
From George Bernard Shaw’s “Maxims for Revolutionists,” 1903:
We are told that when Jehovah created the world he saw that it was good. What would he say now?
Youth, which is forgiven everything, forgives itself nothing: age, which forgives itself everything, is forgiven nothing.
Mens sana in corpore sano is a foolish saying. The sound body is a product of the sound mind.
The reformer for whom the world is not good enough finds himself shoulder to shoulder with him that is not good enough for the world.
Beware of the man who does not return your blow: he neither forgives you nor allows you to forgive yourself.
In moments of progress the noble succeed, because things are going their way: in moments of decadence the base succeed for the same reason: hence the world is never without the exhilaration of contemporary success.
If you injure your neighbor, better not do it by halves.
Two starving men cannot be twice as hungry as one; but two rascals can be ten times as vicious as one.
Decadence can find agents only when it wears the mask of progress.
Do not mistake your objection to defeat for an objection to fighting, your objection to being a slave for an objection to slavery, your objection to not being as rich as your neighbor for an objection to poverty. The cowardly, the insubordinate, and the envious share your objections.
It is dangerous to be sincere unless you are also stupid.
If history repeats itself, and the unexpected always happens, how incapable must Man be of learning from experience!
n. the eating of leeks