When Einstein was traveling to lecture in Spain,
He questioned a conductor again and again:
“It may be a while,”
He asked with a smile,
“But when does Madrid reach this train?”
A Puzzle Book
The world’s most beautiful book is also its most mysterious. The Hypnerotomachia Poliphili, published anonymously in 1499, recounts the “struggle for love in a dream” of Poliphilo, who pursues his beloved Polia through 370 pages of gorgeous woodcuts and epoch-making typography. Their story is told in a cryptic polyglot text of Tuscan, Latin, Greek, Hebrew, and Arabic, replete with arcane references and hidden meanings.
“The Hypnerotomachia is a catalogue of every possible and imaginable foil to understanding,” writes Liane LeFavre in her 2005 exploration of the text. “On every page one is confronted by words whose meaning must be deciphered, inscriptions that have to be interpreted, episodes whose conclusion is ambiguous, a hero and a heroine who embody ideas that have to be divined. Texts and images in code, symbolic images and their interpretation, are recurrent patterns in these cryptic tactics.”
The author’s enormous erudition continually interrupts his story: He fills 200 pages with architectural descriptions and another 60 with botanical lore. The book’s patron, Leonardo Crasso, wrote that it contains “so much science that one would search in vain through all the ancient books [for its meaning], as is the case for many occult things of nature.” The author, he wrote, “devised his work so that only the wise may penetrate the sanctuary.”
Why would anyone produce such a prodigious work of art and learning and then conceal his identity? No one knows for certain. A century and a half after its publication, a French reader discovered an acrostic concealed in the first letters of the book’s 39 chapters. These spell out “Poliam Frater Francescus Columnia Peramavit,” or “Brother Francesco Colonna loved Polonna immensely.” Who was Francesco Colonna? There are two candidates by that name, a Venetian friar and a Roman aristocrat. But both lived on for decades after 1499 and neither claimed to be author of this remarkable book. His identity, and that of the illustrator, remain uncertain.
Choice and Fiction
Raymond Queneau’s A Hundred Thousand Billion Poems consists of 10 sonnets with the same rhyming sounds, so that their 140 lines can be combined into 1014 different poems. Here’s an interactive version.
Milorad Pavić’s 1984 “lexicon novel” Dictionary of the Khazars consists of three miniature encyclopedias that cross-reference one another. Together they document, from varying perspectives, the causes of the disappearance of the Khazar empire in the eighth century. “Each reader will put together the book for himself, as in a game of dominoes or cards, and, as with a mirror, he will get out of this dictionary as much as he puts into it, for you … cannot get more out of the truth than what you put into it.”
Julio Cortázar’s 1963 “counter-novel” Hopscotch can be read in two ways: The reader can advance through the 56 chapters in conventional order or according to an alternate order laid out by the author, which incorporates 99 “expandable chapters” supplied at the end of the book. Thus the novel “consists of many books, but two books above all.”
Georges Perec’s 1978 novel Life A User’s Manual concerns the lives of the inhabitants of a fictional Paris apartment house. Perec structured the novel by lifting off the building’s facade and mapping its rooms onto a 10×10 grid. He then placed an imaginary chess knight on a central square and worked out a tour that took the knight to every location in the building:
He used a similar technique to assign “elements” to each chapter: furniture, animals, clothes, jewels, music, books, toys, flowers, and more were salted into the building’s rooms according to the same rules. “With so much of its material predetermined,” wrote Perec biographer David Bellos, “the place of each chapter in the novel’s sequence, the place of each room described in the block of flats, and forty-two different things to say about every room — surely the book would just write itself.”
In fact Perec wrote it in 18 months. “Writing a novel is not like narrating something related directly to the real world,” he wrote. “It’s a matter of establishing a game between reader and writer.”
Podcast Episode 11: A Woolf in Sheikh’s Clothing
Irish practical joker Horace de Vere Cole orchestrated his masterpiece in 1910: He dressed four friends as Abyssinian princes and inveigled a tour of a British battleship. One of the friends, improbably, was Virginia Woolf (far left) disguised in a false beard and turban. We’ll describe how the prank was inspired and follow the six through their tension-filled visit to the HMS Dreadnought.
We’ll also examine the value of whistles to Benjamin Franklin and present the next Futility Closet Challenge.
Unquote
I own that I cannot see as plainly as others do, and as I should wish to do, evidence of design and beneficence on all sides of us. There seems to me too much misery in the world. I cannot persuade myself that a beneficent and omnipotent God would have designedly created the Ichneumonidae with the express intention of their feeding within the living bodies of Caterpillars, or that a cat should play with mice.
— Charles Darwin, letter to Asa Gray, May 22, 1860
World View
In Other Inquisitions, Borges writes of a strange taxonomy in an ancient Chinese encyclopedia:
On those remote pages it is written that animals are divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g), stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel’s hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.
This is fanciful, but it has the ring of truth — different cultures can classify the world in surprisingly different ways. In traditional Dyirbal, an aboriginal language of Australia, each noun must be preceded by a variant of one of four words that classify all objects in the universe:
- bayi: men, kangaroos, possums, bats, most snakes, most fishes, some birds, most insects, the moon, storms, rainbows, boomerangs, some spears, etc.
- balan: women, bandicoots, dogs, platypus, echidna, some snakes, some fishes, most birds, fireflies, scorpions, crickets, the hairy mary grub, anything connected with water or fire, sun and stars, shields, some spears, some trees, etc.
- balam: all edible fruit and the plants that bear them, tubers, ferns, honey, cigarettes, wine, cake
- bala: parts of the body, meat, bees, wind, yamsticks, some spears, most trees, grass, mud, stones, noises and language, etc.
“The fact is that people around the world categorize things in ways that both boggle the Western mind and stump Western linguists and anthropologists,” writes UC-Berkeley linguist George Lakoff in Women, Fire, and Dangerous Things (1987). “More often than not, the linguist or anthropologist just throws up his hands and resorts to giving a list — a list that one would not be surprised to find in the writings of Borges.”
Beneath the Surface
In Syntactic Structures (1957), to illustrate the difference between a meaningful sentence and a grammatical one, Noam Chomsky offered the expression Colorless green ideas sleep furiously as an example of a grammatical sentence that’s nonsense.
Naturally, some readers took this as a challenge — within months, students at Stanford had set up a competition to show that the expression could be understood as a meaningful sentence. Here’s one of the prizewinning entries:
It can only be the thought of verdure to come, which prompts us in the autumn to buy these dormant white lumps of vegetable matter covered by a brown papery skin, and lovingly to plant them and care for them. It is a marvel to me that under this cover they are labouring unseen at such a rate within to give us the sudden awesome beauty of spring flowering bulbs. While winter reigns the earth reposes but these colourless green ideas sleep furiously.
More entries are here. From David Bellos, Is That a Fish in Your Ear?, 2011.
In a Word
febrifacient
adj. producing fever
The 1895 meeting of the Association of American Physicians saw a sobering report: Abraham Jacobi presented the case of a young man whose temperature had reached 149 degrees.
Nonsense, objected William Henry Welch. Such an observation was impossible. He recalled a similar report in the Journal of the American Medical Association (March 31, 1891) in which a Dr. Galbraith of Omaha had found a temperature of 171 degrees in a young woman.
“I do not undertake to explain in what way deception was practised, but there is no doubt in my mind that there was deception,” he said. “Such temperatures as those recorded in Dr. Galbraith’s and Dr. Jacobi’s cases are far above the temperature of heat rigor of mammalian muscle, and are destructive of the life of animal cells.”
Jacobi defended himself: Perhaps medicine simply hadn’t developed a theory to account for such things. But another physician told Welch that Galbraith’s case at least had a perfectly satisfactory explanation — another doctor had caught her in “the old-fashioned trick of heating the thermometer by a hot bottle in the bed.”
A Full Life
Indeed, death can coexist with immortality. Consider Miss Paginate. She is born in 2000. In 2030 she time travels to a future funeral in 2050. She finds herself in the coffin as a fifty-year-old. Just as a distinction between temporal parts allows you to both sit and stand, it also allows Miss Paginate to be both dead and alive. Indeed, by slowing down her aging to an asymptotic rate from 31 to 39, Miss Paginate lives forever. At age 40, she finds herself back in 2040. She learns that she has been missing from 2031 to 2039. Miss Paginate also discovers that her normal rate of aging has resumed. She commences a memoir of her life, with special attention to the infinite portion that commences from 2050. She regrets her upcoming death in 2050. That will deprive her the time needed to complete her autobiography. But she takes comfort in knowing that she will live forever after her death (albeit as something akin to a partial amnesiac — since she will not remember her experiences from forty to fifty).
— Roy Sorensen, “The Symmetry Problem,” in The Oxford Handbook of Philosophy of Death, 2013
Self-Tiling Tile Sets
These tiles have a remarkable property — by working together, the four can impersonate any one of their number (click to enlarge):
The larger versions could then perform the same trick, and so on. Here’s another set:
In this set, each of the six pieces is paved by some four of them:
By the fathomlessly imaginative Lee Sallows. There’s more in his article “More on Self-Tiling Tile Sets” in last month’s issue of Mathematics Magazine.