An optical illusion. These circles are concentric.
(Baingio Pinna and Richard L. Gregory, “Shifts of Edges and Deformations of Patterns,” Perception 31:12 [December 2002], 1503-1508.)
Bullseye
Busy
Franz Liszt’s 1851 étude “La Campanella” is one of the most technically demanding pieces ever written for piano.
In bar 102, below, the left hand has to jump 35 half-steps, nearly three octaves, in the space of a sixteenth note.
That’s about 46 centimeters.
Org Chart
Say what you will about hell, it’s very well organized. According to the 17th-century grimoire Ars Goetia, the underworld is ruled by 72 demons, each with its own sigil (above) and served by a sort of infernal bureaucracy:
Aim (also Aym or Haborym) is a Great Duke of Hell, very strong, and rules over twenty-six legions of demons. He sets cities, castles and great places on fire, makes men witty in all ways, and gives true answers concerning private matters. He is depicted as a man (handsome to some sources), but with three heads, one of a serpent, the second of a man, and the third of a cat to most authors, although some say of a calf, riding a viper, and carrying in his hand a lit firebrand with which he sets the requested things on fire.
Wikipedia has a page explaining who does what.
Related: Belphegor’s prime, 1000000000000066600000000000001, is a palindromic prime number with 666 at its heart and 13 zeros on either side. It was discovered by Harvey Dubner; Clifford Pickover named it after a prince of hell responsible for helping people make ingenious inventions and discoveries.
Signing Off
When Qantas’ last Boeing 747 departed Australia to retire in the United States, it drew a kangaroo with its flight path.
Unquote
“We discover in ourselves what others hide from us, and we recognize in others what we hide from ourselves.” — Vauvenargues
Half Measures
A problem from the January-February 1991 issue of Quantum:
Prove that the area of the yellow rectangle is half that of the full octagon.
Bother
Apocryphal but entertaining: Allegedly the Duke of Wellington sent this letter to the British War Office during the Peninsular War of 1808-1814:
Gentlemen:
Whilst marching to Portugal to a position which commands the approach to Madrid and the French forces, my officers have been diligently complying with your request which has been sent by H. M. ship from London to Lisbon and then by dispatch rider to our headquarters.
We have enumerated our saddles, bridles, tents, and tent poles, and all manner of sundry items for which His Majesty’s Government holds me accountable. I have dispatched reports on the character, wit, and spleen of every officer. Each item and every farthing has been accounted for, with two regrettable exceptions for which I beg your indulgence.
Unfortunately, the sum of one shilling and ninepence remains unaccounted for in one infantry battalion’s petty cash and there has been a hideous confusion as to the number of jars of raspberry jam issued to one cavalry regiment during a sandstorm in western Spain. This reprehensive carelessness may be related to the pressure of circumstances since we are at war with France, a fact which may have come as a bit of a surprise to you gentlemen at Whitehall.
This brings me to my present purpose, which is to request elucidation of my instructions from His Majesty’s Government, so that I may better understand why I am dragging an army over these barren plains. I construe that perforce it must be one of two alternative duties, as given below. I shall pursue either one with the best of my ability but I cannot do both:
- To train an army of uniformed British clerks in Spain for the benefit of the accountants and copy-boys in London, or perchance
- To see to it that the forces of Napoleon are driven out of Spain.
Your most obedient servant,
Wellington
Black and White
Thomas Taverner published this remarkable problem in the Dubuque Chess Journal in 1889. White is to mate in two moves.
Noted
Sir,
The hymn ‘Onward Christian Soldiers’, sung to the right tune and in a not-too-brisk tempo, makes a very good egg timer. If you put the egg into boiling water and sing all five verses and chorus, the egg will be just right when you come to Amen.
— Mrs. G.H. Moore, letter to the Daily Telegraph, 1983
Arithmetic
Writing home from Princeton in 1939, 21-year-old Richard Feynman challenged his father to solve “this problem in long division. Each of the dots represents some digit (any digit). Each of the A’s represent the same digit (for example, a 3). None of the dots are the same as the A (i.e., no dot can be a 3 if A is 3).”
We don’t know whether his father succeeded — the solution is quite involved: