The Erdős–Faber–Lovász Conjecture

https://commons.wikimedia.org/wiki/File:Erd%C5%91s%E2%80%93Faber%E2%80%93Lov%C3%A1sz_conjecture.svg

This figure contains four “cliques” of four points each, with each of the four points in each clique connected to each of the others, and each pair of cliques intersecting at a single point. Four colors suffice to color all the points so that no two linked points share a color.

Is this always possible? If k cliques, each containing k points, are arranged in similar fashion, can the result always be colored properly with k colors? In 2021, half a century after Paul Erdős first posed the question, Dong Yeap Kang and his colleagues proved that, for sufficiently large k, the conjecture is true.

| Science & Math

Noted

“A few precepts to repeat whenever you are in need of comfort,” by Gabriel Hanotaux, French minister of foreign affairs from 1894 to 1895:

  1. Anything can happen.
  2. Everything is forgotten.
  3. Every difficulty can be overcome.
  4. No one understands anything.
  5. If everyone knew what everyone said about everyone, no one would speak to anyone.

“Above all things, never be afraid. The enemy who forces you to retreat is himself afraid of you at that very moment.”

(Via André Maurois’ The Art of Living, 1939.)

| Society

Second Coming

Lord Dudley was one of the most absent men I think I ever met in society. One day he met me in the street, and invited me to meet myself. ‘Dine with me to-day; dine with me, and I will get Sydney Smith to meet you.’ I admitted the temptation he held out to me, but said I was engaged to meet him elsewhere.

— Wit and Wisdom of Sydney Smith, 1856

| Humor

Casualties

In May 1884, a group of schoolboys on a beach in Zanzibar came upon a large mass of pumice stone that had washed up at the tidemark. Evidently it had been floating in the sea for some time, as its bottom was crusted with barnacles and weed. Welded to its upper surface, they discovered, were dozens of skeletons, including humans, monkeys, and two big cats, probably Sumatran tigers.

It was a relic of the eruption of Krakatoa, which had taken place nine months earlier in the Dutch East Indies. The rock had floated 4,000 miles across the Indian Ocean to the east coast of Africa.

(From Simon Winchester’s Krakatoa, 2013.)

| Oddities

The Beautiful City

https://commons.wikimedia.org/wiki/File:The_Relation_of_the_Individual_to_the_State_by_John_La_Farge.png

Plato’s Republic itself does not begin, as some of the modern writers would have it, with some such sentence as, ‘Human civilization, as seen through its successive stages of development, is a dynamic movement from heterogeneity to homogeneity,’ or some other equally incomprehensible rot. It begins rather with the genial sentence: ‘I went down yesterday to the Piraeus, with Glauco, the son of Aristo, to pay my devotion to the goddess; and desirous, at the same time, to observe in what manner they would celebrate the festival, as they were now to do it for the first time.’

— Lin Yutang, The Importance of Living, 1937

| Language · Literature

Decalogue

Jonathan Franzen’s “10 rules for novelists”:

  1. The reader is a friend, not an adversary, not a spectator.
  2. Fiction that isn’t an author’s personal adventure into the frightening or the unknown isn’t worth writing for anything but money.
  3. Never use the word then as a conjunction — we have and for this purpose. Substituting then is the lazy or tone-deaf writer’s non-solution to the problem of too many ands on the page.
  4. Write in third person unless a really distinctive first-person voice offers itself irresistibly.
  5. When information becomes free and universally accessible, voluminous research for a novel is devalued along with it.
  6. The most purely autobiographical fiction requires pure invention. Nobody ever wrote a more autobiographical story than The Metamorphosis.
  7. You see more sitting still than chasing after.
  8. It’s doubtful that anyone with an Internet connection at his workplace is writing good fiction.
  9. Interesting verbs are seldom very interesting.
  10. You have to love before you can be relentless.

(From The End of the End of the Earth: Essays, 2018.)

| Literature

Swivel Engineering

The Wallace–Bolyai–Gerwien theorem, first proven in 1807, states that any two polygons of equal area must have a common dissection. That is, there’s always a way to cut up the first one and assemble the pieces to form the second.

But what if the pieces must be connected by hinges? In his “haberdasher” puzzle of 1907, Henry Dudeney showed that it’s possible to convert a triangle into a square by cutting it in pieces and turning it “inside out”:

https://commons.wikimedia.org/wiki/File:Hinged_haberdasher_square.svg
Image: Wikimedia Commons

Is it always possible to arrange such a “hinged dissection” between two polygons of equal area? The question remained open until 2007, when Erik Demaine showed that the answer is yes — and provided an algorithm to find it.

| Science & Math

Amen

The day returns and brings us the petty round of irritating concerns and duties. Help us to play the man, help us to perform them with laughter and kind faces, let cheerfulness abound with industry. Give us to go blithely on our business all this day, bring us to our resting beds weary and content and undishonoured, and grant us in the end the gift of sleep.

— Morning prayer recited by Robert Louis Stevenson to his household at Villa Vailima, his last residence in Samoa

| Literature

Redux

https://commons.wikimedia.org/wiki/File:Jean-Antoine_Houdon,_Voltaire,_1778,_NGA_1266.jpg

Jean-Antoine Houdon’s 1778 bust of Voltaire both does and doesn’t appear in Salvador Dalí’s 1940 painting Slave Market.

Dalí said his aim was “to make the abnormal look normal and the normal look abnormal.”

| Art