Round Trip

Looking for a nimble way to transport large amounts of cargo across bodies of water, Alessandro Dandini invented this “spherical rolling hull marine vessel” in 1974. The sphere contains a motor that trundles along a continuous track, which sets the hull rolling across the water. Cargo can be stored inside the sphere, in the two cabins mounted on the sides, or suspended beneath them. (The detachable cabins can also serve as life craft.) Because the sphere has a relatively low draft, it can move through the water with less drag than a conventional vessel. “It provides for a fast turnaround when loading and unloading cargo, which results in a highly efficient water transportation vessel.”

Text Hexes

Books were so precious in the Middle Ages that monks invoked curses against any who might steal them:

This book belongs to S. Maximin at his monastery of Micy, which abbat Peter caused to be written, and with his own labour corrected and punctuated, and on Holy Thursday dedicated to God and S. Maximin on the altar of S. Stephen, with this imprecation that he who should take it away from thence by what device soever, with the intention of not restoring it, should incur damnation with the traitor Judas, with Annas, Caiaphas, and Pilate. Amen.

Should anyone by craft or any device whatever abstract this book from this place may his soul suffer, in retribution for what he has done, and may his name be erased from the book of the living and not be recorded among the Blessed.

This book belongs to S. Alban. May whosoever steals it from him or destroys its title be anathema. Amen.

May whoever destroys this title, or by gift or sale or loan or exchange or theft or by any other device knowingly alienates this book from the aforesaid Christ Church, incur in this life the malediction of Jesus Christ and of the most glorious Virgin His Mother, and of Blessed Thomas, Martyr. Should however it please Christ, who is patron of Christ Church, may his soul be saved in the Day of Judgment.

These are from The Care of Books, by John Willis Clark, 1901. Happily, in 1212 a council met at Paris to decree that “We forbid those who belong to a religious Order, to formulate any vow against lending their books to those who are in need of them; seeing that to lend is enumerated among the principal works of mercy. … From the present date no book is to be retained under pain of incurring a curse, and we declare all such curses to be of no effect.”

Holy War

A letter from Pope Innocent IV to Güyük Khan, king of the Mongols, March 13, 1245:

Seeing that not only men but even irrational animals, nay, the very elements which go to make up the world machine, are united by a certain innate law after the manner of the celestial spirits, all of which God the Creator has divided into choirs in the enduring stability of peaceful order, it is not without cause that we are driven to express in strong terms our amazement that you, as we have heard, have invaded many countries belonging both to Christians and to others and are laying them waste in a horrible desolation, and with a fury still unabated you do not cease from stretching out your destroying hand to more distant lands, but, breaking the bond of natural ties, sparing neither sex nor age, you rage against all indiscriminately with the sword of chastisement.

We, therefore, following the example of the King of Peace, and desiring that all men should live united in concord in the fear of God, do admonish, beg and earnestly beseech all of you that for the future you desist entirely from assaults of this kind and especially from the persecution of Christians, and that after so many and such grievous offences you conciliate by a fitting penance the wrath of Divine Majesty, which without doubt you have seriously aroused by such provocation; nor should you be emboldened to commit further savagery by the fact that when the sword of your might has raged against other men Almighty God has up to the present allowed various nations to fall before your face; for sometimes He refrains from chastising the proud in this world for the moment, for this reason, that if they neglect to humble themselves of their own accord He may not only no longer put off the punishment of their wickedness in this life but may also take greater vengeance in the world to come.

On this account we have thought fit to send to you our beloved son and his companions the bearers of this letter, men remarkable for their religious spirit, comely in their virtue and gifted with a knowledge of Holy Scripture; receive them kindly and treat them with honour out of reverence for God, indeed as if receiving us in their persons, and deal honestly with them in those matters of which they will speak to you on our behalf, and when you have had profitable discussions with them concerning the aforesaid affairs, especially those pertaining to peace, make fully known to us through these same Friars what moved you to destroy other nations and what your intentions are for the future, furnishing them with a safe-conduct and other necessities on both their outward and return journey, so that they can safely make their way back to our presence when they wish.

Güyük wrote back:

By the power of the Eternal Heaven, we are the all-embracing Khan of all the Great Nations. It is our command:

This is a decree, sent to the great Pope that he may know and pay heed.

After holding counsel with the monarchs under your suzerainty, you have sent us an offer of subordination which we have accepted from the hands of your envoy.

If you should act up to your word, then you, the great Pope, should come in person with the monarchs to pay us homage and we should thereupon instruct you concerning the commands of the Yasak.

Furthermore, you have said it would be well for us to become Christians. You write to me in person about this matter, and have addressed to me a request. This, your request, we cannot understand.

Furthermore, you have written me these words: ‘You have attacked all the territories of the Magyars and other Christians, at which I am astonished. Tell me, what was their crime?’ These, your words, we likewise cannot understand. Chinggis Khan and Ogatai Khakan revealed the commands of Heaven. But those whom you name would not believe the commands of Heaven. Those of whom you speak showed themselves highly presumptuous and slew our envoys. Therefore, in accordance with the commands of the Eternal Heaven, the inhabitants of the aforesaid countries have been slain and annihilated. If not by the command of Heaven, how can anyone slay or conquer out of his own strength?

And when you say: ‘I am a Christian. I pray to God. I arraign and despise others,’ how do you know who is pleasing to God and to whom He allots His grace? How can you know it, that you speak such words?

Thanks to the power of the Eternal Heaven, all lands have been given to us from sunrise to sunset. How could anyone act other than in accordance with the commands of Heaven? Now your own upright heart must tell you: ‘We will become subject to you, and will place our powers at your disposal.’ You in person, at the head of the monarchs, all of you, without exception, must come to tender us service and pay us homage; then only will we recognize your submission. But if you do not obey the commands of Heaven, and run counter to our orders, we shall know that you are our foe.

That is what we have to tell you. If you fail to act in accordance therewith, how can we forsee what will happen to you? Heaven alone knows.

The two never met on the field of battle, so God was unable to make his wishes clearer.

(Thanks, Julian.)

Animal Behavior

Martian snakes are elastic. If you take the tail of a Martian snake, and I take the head, and we pull in opposite directions, will there always be a part of the snake that doesn’t move?

Click for Answer


  • Alexander Pope was 4 foot 6.
  • 6! × 7! = 10!
  • Is the correct answer to this question no?
  • “Do something well, and that is quickly enough.” — Baltasar Gracián

A Lost Appeal

A letter from Virginia slave Sargry Brown to her husband Mores, Oct. 27, 1840:

Dear Husband —

this is the third letter that I have written to you, and have not received any from you; and dont no the reason that I have not received any from you. I think very hard of it. the trader has been here three times to Look at me. I wish that you would try to see if you can get any one to buy me up there. if you don’t come down here this Sunday, perhaps you wont see me any more. Give my love to them all, and tell them all that perhaps I shan’t see you any more. Give my love to your mother in particular, and to mamy wines, and to aunt betsy, and all the children; tell Jane and Mother they must come down a fortnight before christmas. I wish to see you all, but I expect I never shall see you all — never no more.

I remain your Dear and affectionate Wife,

Sargry Brown

It never reached him — it was discovered in the dead letter office in Washington, D.C.

The Hypergame Paradox

Call a game finite if it terminates in finitely many moves. Now consider Hypergame, which has two rules:

  1. The first player names a finite game.
  2. The two players play that game.

Is Hypergame a finite game? It seems so: It consists of a single game-naming move, followed by a subgame with a necessarily finite number of moves. But what if the first player names Hypergame itself as the subgame, and the second player names Hypergame as the sub-sub-game, and so on?

In presenting this question to students and colleagues at Union College, mathematician William Zwicker found that many saw the catch and quickly pointed out that it leads to infinite play, thinking that this settles the matter. But the proof that Hypergame is finite seems sound. “I … have to convince them that mathematicians cannot simply abandon a proof once a counter-example has been found, for if the internal flaw in such a proof cannot be identified then the counterexample threatens the entire edifice of mathematical proof.” What is the answer?

(William S. Zwicker, “Playing Games with Games: The Hypergame Paradox,” American Mathematical Monthly 94:6, 507-514)


“There are two things to aim at in life: first, to get what you want; and, after that, to enjoy it. Only the wisest of mankind achieve the second.” — Logan Pearsall Smith


A Hungarian problem shortlisted for the 30th International Mathematical Olympiad, 1989:

Around a circular race track are n race cars, each at a different location. At a signal, each car chooses a direction and begins to drive at a constant speed that will take it around the course in 1 hour. When two cars meet, both reverse direction without loss of speed. Show that at some future moment all the cars will be at their original positions.

Click for Answer

Plant Food

man-eating tree

Exploring a tabooed piece of land on Mindanao, Mississippian planter W.C. Bryant discovered a 35-foot tree surrounded by bones and the smell of carrion. He was entering the circle to examine a skull when his guide suddenly pinioned his arms and pulled him backward “with the strength of a maniac.” Bryant followed the man’s gaze and saw that “the tree was reaching for him”:

The whole thing had changed shape and was horribly alive and alert. The dull, heavy leaves had sprung from their compact formation and were coming at him from all directions, advancing on the ends of long vine-like stems which stretched across like the necks of innumerable geese and, now that the old man had stopped his screaming, the air was full of hissing sounds.

The leaves did not move straight at their target, but with a graceful, side-to-side sway, like a cobra about to strike. From the far side, the distant leaves were peeping and swaying on their journey around the trunk and even the tree top was bending down to join in the attack. The bending of the trunk was spasmodic and accompanied by sharp cracks.

The effect of this advancing and swaying mass of green objects was hypnotic, like the charm movements of a snake. Bryant could not move, though the nearest leaf was within an inch of his face. He could see that it was armed with sharp spines on which a liquid was forming. He saw the heavy leaf curve like a green-mittened hand, and as it brushed his eyebrows in passing he got the smell of it — the same animal smell that hung in the surrounding air. Another instant and the thing would have had his eyes in its sticky, prickly grasp, but either his weakness or the brown man’s strength threw them both on their backs.

The charm was broken. They crawled out of the circle of death and lay panting in the grass while the malignant plant, cracking and hissing, yearned and stretched and thrashed to get at them.

That’s from “Escaped From the Embrace of the Man-Eating Tree,” in the American Weekly, Jan. 4, 1925. Interestingly, naturalist Williard Clute tracked down the author and published a followup in American Botanist that April:

“The author of this tale, having been questioned, replies under date of January 8, 1925, that ‘the tree is there and in the main the account is true. The circle at the foot of the tree was about 80 maybe 100 feet in diameter. The tree looked nothing like the drawings [in the paper]. It was round as a smoke stack — the trunk, I mean, and dark gray or ash-color. The whole tree was symmetrical and the tree and ground under it, was very inviting to a storm-beset or sun-depressed traveller. The clucking and hissing was, I judged, from a gluey consistency of, or on, the leaves. My impression was that if it reached me, it would fasten and hold me, thus it had done to apes, birds, and animals.'” Stay out of the Philippines, I guess.