Image: Flickr

“If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, each of us will have two ideas.” — George Bernard Shaw

“He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point.” — Thomas Jefferson

Podcast Episode 217: The Bone Wars


The end of the Civil War opened a new era of fossil hunting in the American West — and a bitter feud between two rival paleontologists, who spent 20 years sabotaging one another in a constant struggle for supremacy. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Bone Wars, the greatest scientific feud of the 19th century.

We’ll also sympathize with Scunthorpe and puzzle over why a driver can’t drive.

See full show notes …

Turn, Turn, Turn

schwartz parity theorem

I just ran across this, offered by Morton C. Schwartz in an old issue of Pi Mu Episilon Journal:

Take any number of zeros and any number of ones and place them in a circle, in any order. Reproduce the circle a second time, concentrically with the first. Rotate either circle, and any number of places. The number of zeros opposite ones will always be even.

(Morton C. Schwartz, “An Amazing Parity Theorem,” Pi Mu Episilon Journal 5:7 [Fall 1972], 338.)


Cape Town artist Philip Barlow depicts “out-of-focus” cityscapes and beach scenes in oil paints. In photography this effect is known as bokeh, the blurring of elements that lie outside the depth of field. Others have said that Barlow renders the world as it might appear to a near-sighted person.

In this sense the subjects of his paintings are not the objects they depict but rather light itself. “The figures in the landscape serve as carriers and reflectors of the light that falls upon them. Bathed in the luminosity, it is my hope that they would become more beautiful. To me, light is the ultimate subject because it embodies the pinnacle of all reality.”

More at his site.

Mostly Cloudy


In James Joyce’s Ulysses, as Bloom attends Dignam’s funeral, an odd thought passes through his mind: “Now who is that lankylooking galoot over there in the macintosh? Now who is he I’d like to know? Now, I’d give a trifle to know who he is. Always someone turns up you never dreamt of.” The interloper’s presence seems significant: “Mr Bloom stood far back, his hat in his hand, counting the bared heads. Twelve. I’m thirteen. No. The chap in the macintosh is thirteen. Death’s number. Where the deuce did he pop out of? He wasn’t in the chapel, that I’ll swear. Silly superstition that about thirteen.”

He turns up again later: “In Lower Mount street a pedestrian in a brown macintosh, eating dry bread, passed swiftly and unscathed across the viceroy’s path.”

And still later: “A man in a brown macintosh springs up through a trapdoor.”

Altogether the mysterious man is mentioned 11 times in the novel. In the Cyclops episode we’re told, “The man in the brown macintosh loves a lady who is dead,” and in Ithaca, a catechism of questions and answers, we’re asked, “What selfinvolved enigma did Bloom risen, going, gathering multicoloured multiform multitudinous garments, voluntarily apprehending, not comprehend? Who was M’Intosh?”

The question has never been answered definitively. But in his Cornell University lectures on Ulysses, Vladimir Nabokov suggested that the “chap in the macintosh” is none other than James Joyce himself. In the library episode, “Scylla and Charybdis,” Stephen Dedalus explains that Shakespeare “has hidden his own name, a fair name, William, in the plays, a super here, a clown there, as a painter of old Italy set his face in a dark corner of his canvas.” This “is exactly what Joyce has done — setting his face in a dark corner of his canvas. The Man in the Brown Macintosh who passes through the dream of the book is no other than the author himself. Bloom glimpses his maker!”


Churchill himself is a talented heckler. Sir William Joynson-Hicks was making a speech before Commons and noticed Churchill shaking his head so vigorously that attention was distracted from the address. ‘I see my right honourable friend shaking his head,’ cried Joynson-Hicks with exasperation. ‘I wish to remind him that I am only expressing my own opinion!’

‘And I wish to remind the speaker that I am only shaking my own head,’ replied Churchill.

— Brisbane Courier-Mail, 1952



During the last visit which [Samuel Johnson] made to Lichfield [in 1781], the friends with whom he was staying missed him one morning at the breakfast-table. On inquiring after him of the servants, they understood he had set off from Lichfield at a very early hour, without mentioning to any of the family whither he was going. The day passed without the return of the illustrious guest, and the party began to be very uneasy on his account, when, just before the supper-hour, the door opened, and the Doctor stalked into the room. A solemn silence of a few minutes ensued, nobody daring to inquire the cause of his absence, which was at length relieved by Johnson addressing the lady of the house in the following manner: ‘Madam, I beg your pardon for the abruptness of my departure from your house this morning, but I was constrained to it by my conscience. Fifty years ago, madam, on this day, I committed a breach of filial piety, which has ever since lain heavy on my mind, and has not till this day been expiated. My father, you recollect, was a bookseller, and had long been in the habit of attending market, and opening a stall for the sale of his books during that day. Confined to his bed by indisposition, he requested me, this time fifty years ago, to visit the market, and attend the stall in his place. But, madam, my pride prevented me from doing my duty, and I gave my father a refusal. To do away the sin of this disobedience, I this day went in a post-chaise to Uttoxeter, and going into the market at the time of high business, uncovered my head, and stood with it bare an hour before the stall which my father had formerly used, exposed to the sneers of the standers-by and the inclemency of the weather; a penance by which I trust I have propitiated Heaven for this only instance, I believe, of contumacy toward my father.’

— Richard Warner, A Tour Through the Northern Counties of England, 1802

The act is commemorated today in the Johnson Memorial, which stands in the Market Place, in the town center.



To create his 1970 novel A Humument, British artist Tom Phillips began with W.H. Mallock’s forgotten 1892 novel A Human Document and drew, painted, and collaged over the pages, leaving a few words showing to tell a new, hitherto unrevealed story. For instance, the title arises from Phillips’ deletion of two central syllables in Mallock’s title, and the protagonist, Bill Toge, can appear only when the word “together” or “altogether” arises in Mallock’s original text.

Even this new text is evolving. Phillips has published five editions of the book, in each of which he replaces certain pages; eventually he hopes to replace every page, creating an entirely new work (or an entirely new version of the same work).

“Can we call what Phillips is doing ‘writing’, or would some other term be better?” asked Adam Smyth in the London Review of Books. “What version of authorship or creativity is at work here? A Humument is a reminder that books are inevitably intertextual — they grow out of older texts — and that all writing involves selecting words from a finite pool: what appears to be a constraint, having to work within the walls of an existing novel, in fact dramatises a condition of literature.”

The full text of the 1970 edition is here.

Room for More

When logician John Venn introduced the famous diagrams that bear his name, he expressed an interest in “symmetrical figures … elegant in themselves.” He thought the “simplest and neatest figure” that showed all possible logical relations among four sets was four equal ellipses arranged like this:

Image: Wikimedia Commons

“It is obvious that we thus get the sixteen compartments that we want, counting, as usual, the outside of them all as one compartment. … The desired condition that these sixteen alternatives shall be mutually exclusive and collectively exhaustive, so as to represent all the component elements yielded by the four terms taken positively and negatively, is of course secured.”

Interestingly, he added that “with five terms combined together ellipses fail us”: Venn believed that it was impossible to create a Venn diagram with five ellipses. Amazingly, that assertion went unchallenged for nearly a century — it was only in 1975 that Branko Grünbaum found a diagram with five ellipses:

Image: Wikimedia Commons

It’s not possible to form a Venn diagram with six or more ellipses. Do we even need one with five? According to Reddit, yes, we do:


(Peter Hamburger and Raymond E. Pippert, “Venn Said It Couldn’t Be Done,” Mathematics Magazine 73:2 [April 2000], 105-110.)


For a puzzlers’ party in 1993, University of Wisconsin mathematician Jim Propp devised a “self-referential aptitude test,” a multiple-choice test in which each question except the last refers to the test itself:

1. The first question whose answer is B is question

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

2. The only two consecutive questions with identical answers are questions

(A) 6 and 7
(B) 7 and 8
(C) 8 and 9
(D) 9 and 10
(E) 10 and 11

3. The number of questions with the answer E is

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

The full 20-question test is here, the solution is here, and an interesting collection of solving routes is here.

(Jim Propp, “Self-Referential Aptitude Test,” Math Horizons 12:3 [February 2005], 35.)