We’ve had some pretty smart presidents. James Garfield devised this proof of the Pythagorean theorem in 1876, while serving in the House of Representatives:
The area of the trapezoid above is
The area of each green triangle is
And the yellow triangle is
So:
Suppose we hold an election with three candidates, X, Y, and Z. And suppose the voters fall into three groups:
Group 1 prefers, in order, X, Y, Z
Group 2 prefers, in order, Y, Z, X
Group 3 prefers, in order, Z, X, Y
Now, if Candidate X wins, his opponents can rightly object that a majority of voters would have preferred Candidate Z. And corresponding arguments can be made against the other candidates. So even though we’ve held a fair election, it’s impossible to establish majority rule.
The Marquis de Condorcet noted this oddity in the 1700s; it’s sometimes known as Condorcet’s paradox.
Epitaph in the churchyard of Llangerrig, Montgomeryshire:
— Charles Bombaugh, Facts and Fancies for the Curious From the Harvest-Fields of Literature, 1860
Phantom ships, as they have been called, have repeatedly been seen by various observers. Mr. Scoresby, in his voyage to Greenland, in 1822, saw an inverted image of a ship in the air, so well defined that he could distinguish by a telescope every sail, the peculiar rig of the ship, and its whole general character, insomuch that he confidently pronounced it to be his father’s ship, the Fame, which it afterwards proved to be.
— Charles Kingsley, The Boys’ and Girls’ Book of Science, 1881
See also The Wizard of Mauritius.
32 – 23 = 3 – 2
Georg Wilhelm Richmann was attending a meeting at the St. Petersburg Academy of Sciences in August 1753 when he heard thunder. He ran home with another man, hoping to record how an insulated rod responded to an electrical storm.
He succeeded, in a way: A ball of lightning leapt from the rod and struck Richmann in the head, killing him instantly and knocking his companion unconscious. That makes Richmann the first person in history to die while conducting electrical experiments.
Joseph Priestley wrote, “It is not given to every electrician to die in so glorious a manner as the justly envied Richmann.” That’s one way to look at it.
“One may be humble out of pride.” — Montaigne
A whimsical letter written by W. S. Gilbert notes ‘a great want’ among poets. ‘I should like to suggest,’ he says, ‘that any inventor who is in need of a name for his invention, would confer a boon on the rhymsters, and at the same time insure himself many gratuitous advertisements, if he would select a word that rhymes to one of the many words in common use, which have but few rhymes or none at all. A few more words rhyming with ‘love’ are greatly wanted; ‘revenge’ and ‘avenge’ have no rhyming word, except ‘Penge’ and ‘Stonehenge’; ‘coif’ has no rhyme at all; ‘starve’ has no rhyme except (oh, irony!) ‘carve’; ‘scarf’ has no rhyme, though I fully expect to be told that ‘laugh,’ ‘calf,’ and ‘half’ are admissible, which they certainly are not.’
— Miscellaneous Notes and Queries, March 1894
Think of a number greater than 1. Double it.
Between these two values is at least one prime number.
A remarkable instance of the salutary effects of atmospheric electricity on the human body is told by the Wolverhampton correspondent of the London ‘Times.’ He states that during a thunder-storm a collier named Bates, who had lost his sight through an accident, was being led home, when a flash of lightning was reflected on the spectacles he was wearing to conceal his disfigurement. After the peal of thunder which followed he complained of pain in his head. The next moment, to his surprise, he found that he had regained possession of his eye-sight. The occurrence caused considerable excitement in the locality.
— Popular Science Monthly, 1889