Intangible Assets

A perplexing story from logician Raymond Smullyan:

Oh, one other thing. I must tell you of a certain great Sage in the East who was reputed to be the wisest man in the world. A philosopher heard about him and was anxious to meet him. It took him fifteen years to find him, but when he finally did, he asked him: ‘What is the best question that can be asked, and what is the best answer that can be given?’ The great Sage replied: ‘The best question that can be asked is the question you have asked, and the best answer that can be given is the answer I am now giving.’

It’s at the very end of his last book, A Mixed Bag, from 2016.

The Other Half
Image: Wikimedia Commons

Friday, September 19. [1777], after breakfast, Dr. Johnson and I set out in Dr. Taylor’s chaise to go to Derby. The day was fine, and we resolved to go by Keddlestone, the seat of Lord Scarsdale, that I might see his lordship’s fine house. I was struck with the magnificence of the building; and the extensive park, with the finest verdure, covered with deer, and cattle, and sheep, delighted me. The number of old oaks, of an immense size, filled me with a sort of respectful admiration; for one of them sixty pounds was offered. The excellent smooth gravel roads; the large piece of water formed by his lordship from some small brooks, with a handsome barge upon it; the venerable Gothic church, now the family chapel, just by the house; in short, the grand group of objects agitated and distended my mind in a most agreeable manner. ‘One should think,’ said I, ‘that the proprietor of all this must be happy.’

‘Nay, Sir,’ said Johnson, ‘all this excludes but one evil — poverty.’

— James Boswell, Life of Samuel Johnson, 1791

Love and Law

Writing in the San Francisco journal The Californian in 1865, Mark Twain answered this inquiry from a reader:

I loved and still love, the beautiful Edwitha Howard, and intended to marry her. Yet during my temporary absence at Benicia, last week, alas! she married Jones. Is my happiness to be thus blasted for life? Have I no redress?

“Of course you have,” Twain answered. He argued that intention is everything in the law — if you call your friend a fool, this is not an insult if you intended it playfully. And killing a man by accident does not constitute murder.

Ergo, if you had married Edwitha accidentally, and without really intending to do it, you would not actually be married to her at all, because the act of marriage could not be complete without the intention. And, ergo, in the strict spirit of the law, since you deliberately intended to marry Edwitha, and didn’t do it, you are married to her all the same — because, as I said before, the intention constitutes the crime. It is as clear as day that Edwitha is your wife, and your redress lies in taking a club and mutilating Jones with it as much as you can. Any man has a right to protect his own wife from the advances of other men.

But you have another alternative — you were married to Edwitha first, because of your deliberate intention, and now you can prosecute her for bigamy, in subsequently marrying Jones.

But there is another phase in this complicated case: You intended to marry Edwitha, and consequently, according to law, she is your wife — there is no getting around that — but she didn’t marry you, and if she never intended to marry you you are not her husband, of course. Ergo, in marrying Jones, she was guilty of bigamy, because she was the wife of another man at the time — which is all very well as far as it goes — but then, don’t you see, she had no other husband when she married Jones, and consequently she was not guilty of bigamy.

Now according to this view of the case, Jones married a spinster, who was a widow at the same time and another man’s wife at the same time, and yet who had no husband and never had one, and never had any intention of getting married, and therefore, of course, never had been married; and by the same reasoning you are a bachelor, because you have never been any one’s husband, and a married man because you have a wife living, and to all intents and purposes a widower, because you have been deprived of that wife, and a consummate ass for going off to Benicia in the first place, while things were so mixed.

“And by this time I have got myself so tangled up in the intricacies of this extraordinary case that I shall have to give up any further attempt to advise you,” he added. “I might get confused and fail to make myself understood. I think I could take up the argument where I left off, and by following it closely awhile, perhaps I could prove to your satisfaction, either that you never existed at all, or that you are dead, now, and consequently don’t need the faithless Edwitha — I think I could do that, if it would afford you any comfort.”

The Wollemi Pine
Image: Wikimedia Commons

In 1994 bushwalker David Noble abseiled off a cliff 150 kilometers northwest of Sydney and found himself in a very deep canyon surrounded by trees with strange serrated leaves and curious bubbly bark.

He took a sample back to his colleagues at the New South Wales National Parks and Wildlife Service and discovered that he’d found one of the greatest living fossils of the 20th century, with roots in the age of dinosaurs 110-120 million years ago. Somehow the species had survived raging brushfires and 17 ice ages, apparently by retreating to a single canyon in a national park.

The location of that canyon has been kept secret to protect the survivors, which numbered only 100 adult trees in three or four patches, but a special auction in 2005 raised more than a million dollars from bidders eager to receive the first trees cultivated from the rare conifers.

Tim Entwistle, executive director of Sydney’s Botanic Gardens Trust, said that when he learned about Noble’s discovery he went through the classic stages of botanical shock: disbelief, amazement, and excitement. “The Wollemi Pine is a unique reminder that the world is full of undiscovered wonders, that there is a lot more to know about our planet and a lot to protect.”

(Richard Allen and Kimbal Baker, Australia’s Remarkable Trees, 2009.)

Mystery Guest

Who is Horatio? He’s described as a friend of Hamlet, a fellow student at Wittenberg. He seems to be Danish, since he speaks of the elder Hamlet as “our King” and of Danes as countrymen.

But he’s not from Elsinore: He’s unfamiliar with Danish court customs and with people such as Laertes and Osric, and he says he’s seen the King only once (and presumably recently, since he recalls that the King’s beard, like his ghost’s, was gray).

Marcellus and Barnardo, like Hamlet, seem to regard Horatio as a learned and trustworthy companion, but he’s not a close friend — Hamlet is surprised to see him and finds his absence from the university puzzling. Hamlet calls him a good friend, but Horatio calls himself Hamlet’s “poor servant ever.”

At the end of the play, Horatio promises to tell his friend’s story to the Norwegian Prince and “report [his] cause aright,” restoring Hamlet’s reputation and honoring his memory. University of Alberta political scientist Leon Harold Craig notes that this seems to mean that Horatio plans to reveal that Hamlet’s seemingly wayward behavior had been feigned. But “can Horatio plausibly explain why Hamlet should think it ‘meet / To put an antic disposition on’? Indeed, does Horatio even know himself?”

(Leon Harold Craig, Philosophy and the Puzzles of Hamlet, 2014.)


Anthony Gormley’s 1999 sculpture Quantum Cloud is well named — it both does and doesn’t present the figure of a man. It’s composed of sections of steel 1.5 meters long, arranged by a computer using a random walk algorithm starting from points on the surface of an enlarged version of the sculptor’s own body. The result manages to suggest a man’s image without quite depicting it.

“How can you convey the fact that the presence of somebody is greater or different from their appearance?” Gormley writes. “The DOMAINS allowed me to evoke the internal space of the body as a field, but are still bound by an invisible skin: I want to extend or ignore the skin.”

It stands now next to the O2 in London.

In a Word

n. the name of a river, lake, sea, or any other body of water

A bizarre exchange from E.S. Turner’s 2012 What the Butler Saw, a social history of servants in English society:

Vain young gentlemen had a way of summoning their valets to answer questions to which they well knew the answer. [Beau] Brummell, when asked by a bore which of the Lakes he liked best, rang for Robinson. ‘Which of the lakes do I admire most, Robinson?’ he asked; and was informed, ‘Windermere, sir.’ ‘Ah, yes, Windermere, so it is. Thank you, Robinson.’


Sherlock Holmes has the reputation of being relentlessly dour — in “The Adventure of the Mazarin Stone” Watson even says that “Homes seldom laughed.” To counter this, A.G. Cooper counted up 292 instances of Holmes’ laughter, and Charles E. Lauterbach and Edward S. Lauterbach even compiled this table:

Frequency Table Showing the Number and Kind of Responses Sherlock Holmes Made to Humorous Situations and Comments in His 60 Recorded Adventures

Smile: 103
Laugh: 65
Joke: 58
Chuckle: 31
Humor: 10
Amusement: 9
Cheer: 7
Delight: 7
Twinkle: 7
Miscellaneous: 19
Total: 316

The explanation, they suggest, is that Watson was deaf.

(A.G. Cooper, “Holmesian Humour,” Sherlock Holmes Journal 6:4 [Spring 1964), 109-113; Charles E. Lauterbach and Edward S. Lauterbach, “The Man Who Seldom Laughed,” Baker Street Journal Christmas Annual No. 5 [1960], 265-271.)

Palindromic Substrings

What’s unusual about this passage from Great Expectations?

It is not much to the purpose whether a gate in that garden wall which I had scrambled up to peep over on the last occasion was, on that last occasion, open or shut. Enough that I saw no gate then, and that I saw one now. As it stood open, and as I knew that Estella had let the visitors out,– for she had returned with the keys in her hand,– I strolled into the garden, and strolled all over it.

It contains a string of 15 letters that reads the same forward and backward:

It is not much to the purpose whether a gate in that garden wall which I had scrambled up to peep over on the last occasion was, on that last occasion, open or shut. Enough that I saw no gate then, and that I saw one now. As it stood open, and as I knew that Estella had let the visitors out,– for she had returned with the keys in her hand,– I strolled into the garden, and strolled all over it.

Reader Eric Harshbarger has been searching for such strings in literary texts. Here are his finds, and here’s a nifty tool he made that will find the longest palindromic substring in a given passage.

(Thanks, Eric.)

12/11/2021 UPDATE: Eric wonders what’s the longest sensible text one might construct that doesn’t contain any such substrings (an example: “We view uncopyrightable material on Wednesdays”). Add your ideas here.


A normal die is painted so that it has four green faces and two red. Then it’s shaken in a cup and thrown repeatedly onto a table. You’re invited to guess which of these three sequences results. If you guess wrong you lose $10; and if you guess right you win $30.

  1. RGRRR

Most people express the preferences 2, 1, 3, in that order. Red is less likely than green, but it predominates in all three sequences, so many subjects explain that sequence 2 is more “balanced,” and therefore more probable. In fact 65 percent of all subjects (excluding expert statisticians and people whose business is probability) show a strong propensity to vote for sequence 2, even when it’s pointed out explicitly that sequence 1 is just sequence 2 minus the first throw — so sequence 2 cannot be more likely!

“The longer the sequence, the less probable it is, independently of its being ‘balanced’ or ‘unbalanced,'” writes Massimo Piattelli-Palmarini in Inevitable Illusions. “This shows how resistant certain cognitive illusions are. Many other more complex examples have been advanced, and these show that even professional statisticians are sometimes subject to the same illusion.”