Nowhere Man

In 1819, as a riposte to David Hume’s skepticism of the Gospel history, Richard Whately published Historic Doubts Relative to Napoleon Bonaparte:

‘But what shall we say to the testimony of those many respectable persons who went to Plymouth on purpose, and saw Buonaparte with their own eyes? must they not trust their senses?’ I would not disparage either the eyesight or the veracity of these gentlemen. I am ready to allow that they went to Plymouth for the purpose of seeing Buonaparte; nay, more, that they actually rowed out into the harbour in a boat, and came alongside of a man-of-war, on whose deck they saw a man in a cocked hat, who, they were told, was Buonaparte. This is the utmost point to which their testimony goes; how they ascertained that this man in the cocked hat had gone through all the marvellous and romantic adventures with which we have so long been amused, we are not told.

“Let those, then, who pretend to philosophical freedom of inquiry, who scorn to rest their opinions on popular belief, and to shelter themselves under the example of the unthinking multitude, consider carefully, each one for himself, what is the evidence proposed to himself in particular, for the existence of such a person as Napoleon Buonaparte: — I do not mean, whether there ever was a person bearing that name, for that is a question of no consequence; but whether any such person ever performed all the wonderful things attributed to him; — let him then weigh well the objections to that evidence, (of which I have given but a hasty and imperfect sketch,) and if he then finds it amount to anything more than a probability, I have only to congratulate him on his easy faith.”

The whole thing is here.

An Old Friend

Finland’s Raahe Museum contains the oldest surviving diving suit in the world, “The Old Gentleman,” an outfit of calf leather that could sustain a man long enough to inspect the bottom of a sailing vessel.

Museum conservator Jouko Turunen made a copy in 1988. Pleasingly, he called it The Young Gentleman.

The River Witham Sword

This 13th-century double-edged sword, possibly of German manufacture, was found in the River Witham, Lincolnshire, in 1825. Inlaid in gold wire along one of its edges is a curious inscription:


It’s been speculated that this is a religious invocation, but its full meaning is not clear. In 2015 the British Library invited readers to offer their thoughts, but no conclusive solution was reached. Medieval historian Marc van Hasselt of Utrecht University says it may be the product of a sophisticated workshop that made swords for the elite, as similar blades have been found throughout Europe. “These similarities go so far as to suggest the same hand in making the inscriptions. However, their contents are still a mystery, regardless of their origins.”


Thus I
Passe by,
And die:
As One,
And gon:
I’m made
A shade,
And laid
I’th grave,
There have
My Cave.
Where tell
I dwell,

— Robert Herrick, “Upon His Departure Hence,” 1648


piecework chess problems

Two ridiculous problems from Arthur Ford Mackenzie’s 1887 book Chess: Its Poetry and Its Prose:

Left: “White to mate without making a move.”

Right: “White to mate in 1/4 of a move.”

Click for Answer

An Elevated Perspective

tetrahedron example

Consider a triangle ABC and three other triangles (ABD1, BCD2, and ACD3) that share common sides with it, and assume that the sides adjacent to any vertex of ABC are equal, as shown. The altitudes of the three outer triangles, passing through D1, D2, and D3 and orthogonal to the sides of ABC, meet in a point.

This can be made intuitive by imagining the figure in three dimensions. Fold each of the outer triangles “up,” out of the page. Their outer vertices will meet at the apex of a tetrahedron. Now if we imagine looking straight down at that apex and folding the sides down again, each of those vertices will follow the line of an altitude (from our perspective) on the way back to its original position, because each follows an arc that’s orthogonal to the horizontal plane and to one of the sides of ABC. The result is the original figure.

(Alexander Shen, “Three-Dimensional Solutions for Two-Dimensional Problems,” Mathematical Intelligencer 19:3 [June 1997], 44-47.)


The symptoms of a typical attack
A clearly ordered sequence seldom lack;
The first complaint is epigastric pain
Then vomiting will follow in its train,
After a while the first sharp pain recedes
And in its place right iliac pain succeeds,
With local tenderness which thus supplies
The evidence of where the trouble lies.
Then only — and to this I pray be wise —
Then only will the temperature rise,
And as a rule the fever is but slight,
Hundred and one or some such moderate height.
‘Tis only then you get leucocytosis
Which if you like will clinch the diagnosis,
Though in my own experience I confess
I find this necessary less and less.

From Zachary Cope, The Diagnosis of the Acute Abdomen in Rhyme, 1947.

More Loops

Further to my March post “A Lucrative Loop,” reader Snehal Shekatkar of S.P. Pune University notes a similar discovery of iterates leading to strange cycles among natural numbers.

Here is a simple example. Take a natural number and factorize it (12 = 2 * 2 * 3), then add all the prime factors (2 + 2 + 3 = 7). If the answer is prime, add 1 and then factorize again (7 + 1 = 8 = 2 * 2 * 2) and repeat (2 + 2 + 2 = 6). Eventually ALL the natural numbers greater than 4 eventually get trapped in cycle (5 -> 6 -> 5). Instead of adding 1 after hitting a prime, if you add some other natural number A, then depending upon A, numbers may get trapped in a different cycle. For example, for A = 19, they eventually get trapped in cycle (5 -> 24 -> 9 -> 6 -> 5).

For some values of A, several cycles exist. For example, when A = 3, some numbers get trapped in cycle (5 -> 8 -> 6 -> 5) while others get trapped in the cycle (7 -> 10 -> 7).

(Made with Tian An Wong of Michigan University.) (Thanks, Snehal.)

The Savage Breast

A logic problem from Lewis Carroll: What conclusion follows from these premises?

  1. Nobody who really appreciates Beethoven fails to keep silent while the Moonlight Sonata is being played.
  2. Guinea pigs are hopelessly ignorant of music.
  3. No one who is hopelessly ignorant of music ever keeps silent while the Moonlight Sonata is being played.
Click for Answer