“If it is feared by a schizophrenic that nothing feared by a schizophrenic is the case, then there must be at least one other schizophrenic fear besides this one.”
— P.T. Geach, quoted in A.N. Prior, “On a Family of Paradoxes,” Notre Dame Journal of Formal Logic, 1961
What’s unusual about these dice is obvious. But what’s normal about them?
When thrown together, they produce the same probability distribution as a pair of ordinary dice. There are six ways to throw a 7, five ways to throw an 8, etc. This the only possible alternate arrangement in which all the face values are positive.
They were discovered/invented by George Sicherman of Buffalo, N.Y.
A solution of glucose, sodium hydroxide, and indigo carmine, when shaken, will change from yellow to red to green. Left to sit, it will revert to red again, then yellow, and the process can be repeated.
The indigo carmine is green when oxidized, yellow when reduced, and red in the intermediate semiquinone state.
Two trick questions:
Who played the title role in Bride of Frankenstein? Valerie Hobson — not Elsa Lanchester.
Did Adlai Stevenson ever win national office? Yes — Adlai Stevenson I served as vice president under Grover Cleveland in 1893.
A tank of water has two holes of equal area, one at top and one at bottom. The top one leads to a downspout, so that both holes discharge their water at the same level. Ignoring friction, which hole produces the faster flow of water?
You actually don’t need to know the physics in order to solve this — it yields to an insight.
Arrange a deck of cards in alternating colors, black and red. Now cut the deck so that the bottom card of one pile is black and the other is red. Riffle-shuffle the two piles together again. Now remove cards from the top of the pack in pairs. How many of these pairs should we expect to contain cards of differing colors?
Surprisingly, all of them will. During the shuffle, suppose a black card falls first. It must be followed by either the next card in its own pile, which is red, or the first card from the other pile, which is also red. Either way, this first pair will contain one black card and one red card, and by the same principle so will each of the other 25 pairs produced by the shuffle. This effect was first identified by mathematician Norman Gilbreath in 1958.
Related: Arrange the deck in a repeating cycle of suits, such as spade-heart-club-diamond, spade-heart-club-diamond, etc. Ranks don’t matter. Now deal about half of this deck onto the table and riffle-shuffle the two halves back together. If you draw cards from the top in groups of four, you’ll find that each quartet contains one card of each suit.
See So Much for Entropy.
A calendar curiosity by Canadian magician Mel Stover:
Offer any month’s calendar to a friend and have him outline a 4×4 square of dates. Ask him to circle any date in that square and cross out the other numbers in its row and column. Have him do this three more times and then add the circled numbers.
You can predict his answer by totaling the numbers in either pair of diagonally opposite corners in the square and doubling that number. Why does this work?
‘Well, do you know the one,’ I began, ‘in which two geologists converse in a cafe? One of them says: ‘Yes, unfortunately fifteen billion years from now the Sun will cool, and then all life on Earth will perish.’ A card-player nearby has been half listening to the joke, and turns in terror to the geologist: ‘What did you say? In how many years will the Sun cool?’ ‘Fifteen billion years,’ the scientist replies. The card-player lets out a sigh of relief: ‘Oh, I was afraid you said fifteen million!’
— László Feleki in Impact of Science on Society, 1969
“Even if I could be Shakespeare, I think I should still choose to be Faraday.” — Aldous Huxley
We were staying in Ballater, a small town on Deeside in Scotland. In the town was a tiny shop which sold tourist attractions and picture postcards, and in its minute window was a very fine specimen of smoky quartz material. Buying a postcard, I said to the proprietor, ‘That’s a fine group of smoky quartz in your window’ and had this reply in very broad Scotch:
‘That’s no smoky quartz, that’s topaz. It’s a crystal. You can tell crystals by the angles between their faces. If you’re interested I’ll lend you a book on the subject.’
I knew enough (crystals being rather in my line) to be sure it was smoky quartz, and on return to base looked up a book on Mineralogy which said ‘Smoky Quartz, also known as Cairngorm, is called Topaz in Scotland.’
— Sir W.L. Bragg, quoted in R.L. Weber, A Random Walk in Science, 1973
