Webster’s New World Dictionary of the American Language defines paradox as “1. a statement that seems contradictory, etc. but may be true in fact. 2. a statement that is self-contradictory and, hence, false.”
(Noted by David Morice in the August 1993 issue of Word Ways.)
In 1988, tunneling operations began in both England and France. On Dec. 1, 1990, these two single-entrance holes met under the English Channel, after which there existed a two-entrance tunnel. The completed Channel Tunnel would not be ready for use until 1994. Now, suppose that a speaker in 1989 had said:
There is in the process of coming into existence, so we understand, the Channel Tunnel. Not many of us have seen it; I certainly have not. One understands that that will allow us, if and when it is made available, to travel by train from England to France.
Does this utterance imply that, at the time it was spoken, the Channel Tunnel already existed? If not, what is the it that the speaker says few people have seen? In 1989 all that existed were two blind tunnels, which together could not permit free passage between England and France, surely an essential feature of the Channel Tunnel.
“In the construction of the Channel Tunnel, the time at which we can say that a two-entrance tunnel first exists is 1st December 1990, when the two one-entrance tunnels met,” notes philosopher Antony Galton. “The Channel Tunnel is a two-entrance tunnel; so is this time, 1st December 1990, also the time at which the Channel Tunnel first exists?”
(Antony Galton, “On the Process of Coming Into Existence,” Monist 89:3 [July 2006], 294-312.)
The first chess-like game played by a computer was this little variant, written for the MANIAC I by Paul Stein and Mark Wells at Los Alamos Scientific Laboratory in 1956. To accommodate the computer’s limitations, there are no bishops (and pawns can’t promote to bishops); pawns can advance only one square on their first move; there is no en passant capture; and there is no castling.
It played three games. In the first it played against itself; in the second, a strong human player gave queen odds and won; and in the third it played against a lab assistant who’d learned the rules of chess only recently. The computer won the last game, marking the first time that a computer beat a human in a chess-like game. Here’s the score:
White: MANIAC I Black: Beginner
1.d3 b4 2.Nf3 d4 3.b3 e4 4.Ne1 a4 5.bxa4 Nxa4 6.Kd2 Nc3 7.Nxc3 bxc3+ 8.Kd1 f4 9.a3 Rb6 10.a4 Ra6 11.a5 Kd5 12.Qa3 Qb5 13.Qa2+ Ke5 14.Rb1 Rxa5 15.Rxb5 Rxa2 16.Rb1 Ra5 17.f3 Ra4 18.fxe4 c4 19.Nf3+ Kd6 20.e5+ Kd5 21.exf6=Q Nc5 22.Qxd4+ Kc6 23.Ne5# [diagram] 1–0
Jami Johnson lost her wallet on December 11, 2007, when she left it on the counter at the Zip Trip convenience store in Clarkston, Washington. A surveillance video showed a man pick it up and walk out of the store with it.
The man, Michael Millhouse, was arrested two days later and charged with theft. How did police catch him so quickly? The Lewiston Tribune had published a frame from the surveillance video on its front page, directly below a four-column photo of Millhouse decorating a local window for the holidays. He was identified by name and was even wearing the same clothing as in the surveillance photo.
Clarkston Police Chief Joel Hastings said, “Initially, Millhouse denied taking the wallet and then said that he had taken the wallet, and thought it was his wife’s wallet. Later he said that he intended turning the wallet in to the police but had forgot about it.”
Police found the wallet at Millhouse’s business, Millhouse Signs of Lewiston, and returned it to Johnson. “This is the most unusual of any one I know of, to have both pictures on the front page at the same time and in the same location,” Hastings said. “I’ve never experienced that anywhere.”
A problem from the Leningrad Mathematical Olympiad: You have a set of 101 coins, and you know that it contains one counterfeit coin X. The 100 genuine coins all have the same weight, which is different from that of X. Using only two weighings in an equal-arm balance, how can you determine whether X is heavier or lighter than the genuine coins?
This 19th-century sculpture manages to find two characters from Goethe’s Faust in a single piece of sycamore.
It resides in the Salar Jung Museum in Hyderabad. The artist is unknown.
In his 1922 book Songs of the Birds, Oxford zoologist Walter Garstang set out to record birdsongs as musical compositions:
The peculiar quality or timbre of each bird’s voice and the resonance of each sound have been imitated as closely as possible by a selection of human consonants; the composition of the song has been represented by the appropriate repetition, modification, or contrast of selected syllables; the syllabic rendering has been cast in a corresponding rhythm; and round this chosen sequence of syllables a song has been woven to capture something, if possible, of the joy or of the attendant circumstances which form the natural setting of his song.
“I fell in love with my models,” he wrote, “and could not content myself with a purely scientific account of their performances.” He was similarly enraptured by amphibians — the 1951 book Larval Forms collects his poems about marine larvae:
Amblystoma’s a giant newt who rears in swampy waters,
As other newts are wont to do, a lot of fishy daughters:
These Axolotls, having gills, pursue a life aquatic,
But, when they should transform to newts, are naughty and erratic.
His colleague Alister Hardy wrote, “I certainly believe that he gets his ideas across with much greater felicity in these sparkling rhymes than he has done in all his more carefully calculated prose.”
See Bird Songs.
NASA’s 2006 Space Technology 5 carried an unusual item — an antenna that had evolved through Darwinian evolution. To meet a challenging set of mission requirements, researchers at New Mexico State University used a computer program to generate simple antenna shapes, altered them in semi-random manner, and evaluated the results. Those that performed worst against design requirements were discarded and the remainder again “mutated” in a process modeled on natural selection. This procedure can produce a complex but highly efficient shape that might not be found using more traditional methods.
“By exploring such a wide range of designs EAs may be able to produce designs of previously unachievable performance,” the team concluded. “The faster design cycles of an evolutionary approach results in less development costs and allows for an iterative ‘what-if’ design and test approach for different scenarios.”
Our servants were devoted to us and took their duties very much to heart. At a time when houses were still lighted by candles and lamps, a considerable staff was needed to attend to the lighting. The manservant who was in charge of the staff was so grieved when electric lighting was introduced that he drowned his sorrows in drink and died from its effects shortly after.
— A childhood memory of Russian aristocrat Felix Yusupov (1887-1967), of the Moika Palace in St. Petersburg, from his 1952 memoir Lost Splendor
If you erect equilateral triangles on two adjacent sides of a square and then connect the triangle vertices distant from the square to the square vertex distant from the triangles, you get a third equilateral triangle.
Pleasingly, this works whether the triangles are erected inside or outside the square. It was discovered by French mathematician Victor Thébault.
