A perpetual-motion scheme from Henry Dircks’ Perpetuum Mobile (1861). Each bellows is fitted with a weight and filled with quicksilver, and a canal connects each opposing pair of bellows. Thus the weights will continually compress the bellows on the left and expand those on the right, forcing the quicksilver always into the rightmost bellows and ensuring that the wheel turns forever. Won’t they?
Imagine yourself to be a surgeon, a truly great surgeon. Among other things you do, you transplant organs, and you are such a great surgeon that the organs you transplant always take. At the moment, you have five patients who need organs. Two need one lung each, two need a kidney each, and the fifth needs a heart. If they do not get those organs today, they will all die; if you find organs for them today, you can transplant the organs and they will all live. But where to find the lungs, the kidneys, and the heart? The time is almost up when a report is brought to you that a young man who has just come into your clinic for his yearly check-up has exactly the right blood-type and is in excellent health. Lo, you have a possible donor. All you need to do is cut him up and distribute his parts among the five who need them. You ask, but he says, ‘Sorry. I deeply sympathize, but no.’ Would it be morally permissible for you to operate anyway?
— Judith Jarvis Thompson, “The Trolley Problem,” Yale Law Journal, 1985
Is a legal chess game possible in which all the pawns promote and each player has nine queens?
Yes — Freidrich Burchard of Germany and Friedrich Hariuc of Romania reached nearly identical solutions in 1980:
1. e4 f5 2. e5 Nf6 3. exf6 e5 4. g4 e4 5. Ne2 e3 6. Ng3 e2 7. h4 f4 8. h5 fxg3 9. h6 g5 10. Rh4 gxh4 11. g5 g2 12. g6 Bg7 13. hxg7 g1=Q 14. f4 h3 15. f5 h2 16. b4 a5 17. b5 a4 18. b6 a3 19. Bb2 Ra7 20. bxa7 axb2 21. a4 b5 22. a5 b4 23. a6 b3 24. c4 h1=Q 25. c5 h5 26. c6 Bb7 27. cxb7 c5 28. d4 c4 29. d5 Nc6 30. dxc6 c3 31. c7 c2 32. c8=Q c1=Q 33. b8=Q Qc7 34. a8=Q d5 35. a7 d4 36. Nc3 dxc3 37. Qa6 c2 38. Qa8b7 c1=Q 39. a8=Q Qd5 40. gxh8=Q+ Kd7 41. g7 bxa1=Q 42. g8=Q b2 43. f7 b1=Q 44. f8=Q h4 45. f6 h3 46. f7 h2 47. Qfa3 h1=Q 48. f8=Q exf1=Q+
This may be the shortest possible such game.
Future civilizations will remember us for one thing: We finally found a way to keep the cereal from getting soggy.
This “crispy cereal serving piece and method,” patented by Alton Davis in 1991, connects two bowls with a chute. “A measured, quickly consumable portion of the cereal can then be urged with a spoon or other eating utensil from the upper bowl down the chute and into the milk, from where it can be consumed before it absorbs sufficient quantities of milk to become soggy.”
Take that, Phoenicians!
Only 43 numbers have names that lack the letter N.
One of them, fittingly, is forty-three.
G stands for gnu,
Whose weapons of defense
Are long, sharp, curling horns, and common sense.
To these he adds a name so short and strong,
That even hardy Boers pronounce it wrong.
How often on a bright autumnal day
The pious people of Pretoria say,
“Come, let us hunt the–” Then no more is heard
But sounds of strong men struggling with a word.
Meanwhile, the distant gnu with grateful eyes
Observes his opportunity and flies.
— Hilaire Belloc
Draw any quadrilateral and connect the midpoints of its sides.
You’ll always get a parallelogram.
Triangles, too, have perfection at heart.
“I know of no rule which holds so true as that we are always paid for our suspicion by finding what we suspect.” — Thoreau
The familiar Mercator projection is useful for navigation, but it exaggerates the size of regions at high latitudes. Greenland, for example, appears to be the same size as South America, when in fact it’s only one eighth as large.
An equal-area projection such as the Mollweide, below, distorts the shapes of regions but preserves their relative size. This reveals some surprising facts: Russia is larger than Antarctica, Mexico is larger than Alaska, and Africa is just mind-bogglingly huge — larger than the former Soviet Union, larger than China, India, Australia, and the United States put together.
A puzzle from L. Despiau’s Select Amusements in Philosophy and Mathematics, 1801:
Distribute among 3 persons 21 casks of wine, 7 of them full, 7 of them empty, and 7 of them half full, so that each of them shall have the same quantity of wine, and the same number of casks.
