“Sweet-Seasoned Showers”

craig knecht -- shakespeare water-retention square

Today marks the 400th anniversary of William Shakespeare’s death. To commemorate it, Craig Knecht has devised a 44 × 44 magic square (click to enlarge). Like the squares we featured in 2013, this one is topographical — if the number in each cell is taken to represent its altitude, and if water runs “downhill,” then a fall of rain will produce the pools shown in blue, recalling the words of Griffith in Henry VIII:

Noble madam,
Men’s evil manners live in brass; their virtues
We write in water.

The square includes cells (in light blue) that reflect the number of Shakespeare’s plays (38) and sonnets (154) and the year of his death (1616).

(Thanks, Craig.)

The Public Figure

In 1956 Macedonian poet Venko Markovski was imprisoned under a fictitious name for circulating a poem critical of Marshal Tito.

Among the guards were individuals who were taking correspondence courses in an attempt to earn a degree. One of these guards, knowing I was a writer, came up to me one day and said: ‘I was told you are a writer. You have knowledge of literature. I have a request …’

‘Please, what do you want to know about literature?’

‘Tell me about Macedonian literature.’

‘Whom are you interested in?’

‘Venko Markovski.’

‘Is it possible you don’t recognize Venko Markovski?’

‘I don’t know him.’

There was an unpleasant pause. I felt sorry for this man who was ordered to guard someone without knowing whom he was guarding. I spoke to him as follows:

‘The best way for you to learn about Venko Markovski is to read his poetry written in Croatian. In this way you will understand Markovski the poet, the Partisan, the public figure, and you will pass your exam easily. But if you rely on me to tell you about Venko Markovski, you will find yourself — after you fail your exam — in the very place where Markovski now finds himself.’

‘What do you mean by that?’ the guard asked. ‘Where is he in fact?’

‘Right in front of you, here on Goli Otok.’

‘Can it be that you are really he?’

‘Yes, I am here under another name.’

The guard walked away silent and confused.

“The warden obviously thought that since he had physical possession of his prisoners he disposed of their minds and souls as well,” Markovski wrote after gaining his freedom in 1961. “But he was mistaken; the body is one thing and the soul is another. There is no way to bribe the human conscience once it has committed itself to the struggle for the rights of its people.”

(From Geoffrey Bould, ed., Conscience Be My Guide: An Anthology of Prison Writings, 2005.)


British infantry sergeant Harry Neale says goodbye to his 10-year-old daughter Lucy, April 4, 1917:

At about six o’clock in the evening, my father called me in and said he’d got to go back to Kidderminster, back to barracks. ‘Will you walk with me a little way, just up the hill, will you come with me?’ Of course I would. He said goodbye to my mother, who was crying, and we went off down the road and then up this long hill. It was a ten-minute walk, I suppose, but we didn’t hurry, we just walked slowly up the hill and I really can’t remember what we talked about. I held on to his hand so tight, and when we got to the top, he said, ‘I won’t take you any further, you must go back now, and I’ll stand here and watch you until you’re out of sight,’ and he put his arms round me and held me so close to him; I remember feeling how rough that khaki uniform was.

‘You must go now, wave to me at the bottom, won’t you?’ I went, I left him standing there and I went down the hill and I kept looking back and waving and he was still there, just standing there. I got to the bottom and then I’d got to turn off to go to where we lived, so I stopped and waved to him and he gestured as much as to say, ‘Go on, you must go home now,’ ever so gently gestured and then he waved and he was still waving when I went, and that was the last time I ever saw him.

Badly wounded in battle, he died of dysentery in East Africa that October.

(From Richard van Emden, The Quick and the Dead, 2011.)

The Outer Limits


In January 2007, inspired by this article by computer scientist Scott Aaronson, philosophers Agustín Rayo of MIT and Adam Elga of Princeton joined in the “large number duel” to come up with the largest finite number ever written on an ordinary-sized chalkboard.

The rules were simple. The two would take turns writing down expressions denoting natural numbers, and whoever could name the largest number would win the duel. No primitive semantic vocabulary was allowed (so that it would be illegal simply to write the phrase “the smallest number bigger than any number named by a human so far”), and the two agreed not to build on one another’s contributions (so neither could simply write “the previous entry plus one”).

Elga went first, writing the number 1. Rayo countered with a string of 1s:


and Elga erased a line through the base of half this string to produce a factorial:


The two began defining their own functions, and toward the end Rayo wrote this phrase:

The smallest number bigger than any number that can be named by an expression in the language of first-order set theory with less than a googol (10100) symbols.

With some tweaking, this became the winning entry, now enshrined as “Rayo’s number.”

“It was a great game,” Elga said after the match. “Heated at times, but nevertheless, a really great game.”

The use of philosophy was “crucial,” Rayo said. “The limit of math ability was reached at the end. Knowing a bit of philosophy, that was the key.”

Asked whether he thought his entry had set the Guinness world record, “It’s hard to be sure,” Rayo said, “but the number is bigger than any number I have ever seen.”

(Thanks, Erik.)

Ruly English

In 1957, the U.S. Patent Office wanted to design a computer that could track down earlier references to an idea submitted by an inventor. This is difficult, because patents are described in ordinary English, which uses many ambiguous and imprecise terms. The word glass, for instance, refers to a material, but also to any number of things made of that material, and even to objects that have nothing to do with glass, such as plastic eyeglasses and drinking glasses.

To solve this problem, engineer-lawyer Simon M. Newman planned a synthetic language called Ruly English that gave one and only one meaning to each word. In ordinary English the preposition through has at least 13 meanings; Newman proposed replacing each of them with a new Ruly term with a single meaning. The Ruly word howby, for example, means “mode of proximate cause.” It might replace the unruly terms by(take by force) or with (to kill with kindness) or through (to cure through surgery), but it always has the same basic sense.

Newman had to coin other terms to take account of differing points of view. A watch spring and a bridge girder are both flexible to some degree, but using the word flexible to describe both would leave a computer at a loss as to how they compare. Newman coined the Ruly word resilrig to cover the whole scale, from extreme flexibility to extreme rigidity, adding prefixes such as sli (slightly) and sub (substantially). So in Ruly English a bridge girder would be sliresilrig and a watch spring subresilrig. A computer that knew these terms would not be confused into thinking that a thin bridge girder was more flexible than a rigid watch spring.

“Humans are not expected to read or speak Ruly English,” noted Time in 1958. “To them, unruly English will always be more ruly.”

(Newman describes his plan briefly here. I don’t know how far he got.)