The Grand Tour

Letter to the London Times, May 15, 1967:

Sir, is it not time that the Governments of great nations ceased to brag about their astronauts orbiting the earth? I have myself circled round the sun eighty times, without any publicity; a far greater achievement. I am in fact, just starting on my eighty-first orbit. And although I am an old man (I was born on May 10, 1887) I have been circling regularly from the day of my birth, if not before; and have suffered no ill effects.

Everyone does it.

Yours faithfully,

Frank Townshend

| Science & Math

Curiosity

English polymath Thomas Browne (1605-1682) was interested in everything, a fact reflected in the wonderful index to his Works, published by William Pickering in 1835:

Apes, incapable of a truly erect posture, i. 379
Bay-leaves, said to be found green in the tomb of St. Humbert, iii. 23
Circles, number of, in the heavens, i. 429, n.
Crocodile, supposed never to cease growing, ii. 258; truth of this, ib. n.
Dread, explanation of the term, iii. 241
Field, a green, described as appearing at the bottom of the Red Sea, explanation of it, iii. 172
Grecian cavalry quincuncially arranged, ii. 510
Happiness, none in this world, ii. 450
Iron, digestion of, by the ostrich, i. 334
Joints of elephants, i. 220
Language, whether children would naturally, and if untaught, speak the primitive language of the world, ii. 91
Lions’ heads, why the common ornament of aqueducts, &c. ii. 85
Meat and drink, whether they go through different passages into the stomach, i. 408
Mist, account of the, which happened Nov. 27, 1674, iii. 339
Owls and ravens deemed ominous, ii. 79; why, ib. n.
Parrots, their screaming, how made, i. 362, n.
Printing, question as to the country of its invention, ii. 357
Rabble, to be found among gentry, ii. 416
Rain, only apparently pure, i. 331
Ribs, whether a man has fewer than a woman, a common conceit; but neither true nor reasonable, and why, ii. 214
Sitting cross-legged unlucky, ii. 84
Storks, that they will only live in free states, i. 360; obviously false, ib.; an hospital at Fez for sick storks, 561
Tulips never blue, ii. 181
Wales, singular boats used in, i. 141
Xenophanes held that the earth has no bottom, i. 114; that there is another world in the moon, 91

The collection was edited by Simon Wilkin.

| Literature

Unawares

From Samuel Butler’s notebooks, 1912:

Those who die suddenly and without warning not only never die (in the sense in which no man ever dies to himself), but never even think they are going to die soon. A man knocked to pieces by a passing train while greasing wheel-boxes does not even leave off greasing wheel-boxes so far as he is himself concerned, but goes on greasing them for ever and ever for such an infinity of time as is practically no time at all. Or how about one who eats a good dinner and goes to sleep after it too near a charcoal fire of which he knew nothing?

Related: You will never enter the grave.

| Death

Vacuous Thinking

https://commons.wikimedia.org/wiki/File:Diagram_of_Pythagoras_Theorem.png

A simple proof of the Pythagorean theorem. On each of these identical square tabletops are arranged four copies of the same right triangle. On the first table, the uncovered space takes the shape of the square of the triangle’s hypotenuse; on the second, it equals the sum of the squares of the triangle’s two smaller sides. The two tabletops are the same size, so these uncovered spaces have the same area.

| Science & Math

Letter Perfect

Anton Pavlis of Guelph, Ontario, devised this monstrous alphametic, which has 41 addends. If each letter consistently stands for a particular digit, what sum does this expression denote?

   SO
 MANY
 MORE
  MEN
 SEEM
   TO
  SAY
 THAT
 THEY
  MAY
 SOON
  TRY
   TO
 STAY
   AT
 HOME
   SO
   AS
   TO
  SEE
   OR
 HEAR
  THE
 SAME
  ONE
  MAN
  TRY
   TO
 MEET
  THE
 TEAM
   ON
  THE
 MOON
   AS
   HE
  HAS
   AT
  THE
OTHER
+ TEN
-----
TESTS

Don’t even try to solve it — here’s the answer:

   31
 2764
 2180
  206
 3002
   91
  374
 9579
 9504
  274
 3116
  984
   91
 3974
   79
 5120
   31
   73
   91
  300
   18
 5078
  950
 3720
  160
  276
  984
   91
 2009
  950
 9072
   16
  950
 2116
   73
   50
  573
   79
  950
19508
+ 906
-----
90393

(From the Journal of Recreational Mathematics, via Crux Mathematicorum, April 1983.)

| Puzzles

Long Distance Runaround

https://commons.wikimedia.org/wiki/File:Infinite_chess_position_with_game_value_%CF%89_(Black_to_move).png
Image: Wikimedia Commons

Played on an unbounded chessboard, “infinite chess” feels familiar but can lead to some strange situations. In this position White threatens to give checkmate by advancing his rook one square. Black can avoid this fate by throwing his rook any finite distance to the north, as shown. Now when White’s rook gives check, Black’s king has room to retreat up the board. But it’s still curiously doomed: By advancing alternately his queen and then his rook by two squares each, repeatedly, White can now harry the Black king indefinitely northward after the departed rook. Because each of White’s moves gives check, Black’s king has no time to do anything but flee, and when it fetches up against the far-flung rook White will finally give checkmate.

Thus, in the diagramed position with Black to move, it’s accurate to say that White has a forced checkmate but that there’s no bound on the number of moves it may take to deliver it.

(C.D.A. Evans and Joel David Hamkins, “Transfinite Game Values in Infinite Chess,” arXiv preprint arXiv:1302.4377 [2013].)

| Science & Math

Whiplash

The dwarf reed snake escapes predators by leaping into a continuous cartwheel that’s four times as fast as slithering.

“The acrobatics involved in rolling are a fascinating example of how much snakes can accomplish with their limbless bodies,” Toho University ecologist Yosuke Kojima told the New York Times.

“It’s nice to be surprised by weird snake behaviour occasionally,” said herpetologist Frank Burbrink. “It is truly remarkable and probably fairly arresting for any predators that encounter these little guys.”

(Yosuke Kojima, et al., “Locomotor Kinematics and Head Stabilization in Rolling Snakes,” Current Biology 36:20 [Oct. 19, 2026], R1061-R1063. Thanks, Sharon.)

| Science & Math