“The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” — F. Scott Fitzgerald
“It is the mark of an educated mind to be able to entertain a thought without accepting it.” — Aristotle
“Education enables you to express assent or dissent in graduated terms.” — William Cory
“Education is the ability to listen to almost anything without losing your temper or your self-confidence.” — Robert Frost
“To change an opinion without a mental process is the mark of the uneducated.” — Geoffrey Madan
“To have doubted one’s own first principles is the mark of a civilized man.” — Oliver Wendell Holmes
When Ewart Grogan was denied permission to marry his sweetheart, he set out to walk the length of Africa to prove himself worthy of her. In this week’s episode of the Futility Closet podcast we’ll find out whether Ewart’s romantic quest succeeded.
We’ll also get an update on the criminal history of Donald Duck’s hometown, and try to figure out how a groom ends up drowning on his wedding night.
By W.A. Shinkman. This is a self-mate in two moves: White makes a move, Black is allowed to make any legal reply, then White plays a second move that forces Black to checkmate him.
A flock of starlings masses near sunset over Gretna Green in Scotland, preparatory to roosting after a day’s foraging. The flock’s shape has a mesmerisingly fluid quality, flowing, stretching, rippling, and merging with itself. Similarly massive flocks form over Rome and over the marshlands of western Denmark, where more than a million migrating starlings form an enormous display known as the “black sun.”
What rules produce this behavior? In the 1970s scientists thought that the birds might be following an electrostatic field produced by the leader. Earler, in the 1930s, one paper even suggested that they use thought transference.
But in 1986 computer graphics expert Craig Reynolds found that he could create a lifelike virtual flock (below) using a surprisingly simple set of rules: direct each bird to avoid crowding nearby flockmates, steer toward the average heading of nearby flockmates, and move toward the center of mass of nearby flockmates.
Studies with real birds seem to bear this out: Under rules like these a flock can react sensitively to a change in direction by any of its members, permitting the whole group to respond efficiently as one organism. “News of a predator’s approach can be communicated rapidly through the flock by whichever of the hundreds of birds on the outside notice it first,” writes Gavin Pretor-Pinney in The Wavewatcher’s Companion. “When under attack by a peregrine falcon, for instance, starling flocks will contract into a ball and then peel away in a ribbon to distract and confuse the predator.”
New Year’s Day normally falls one week after Christmas: If Christmas falls on a Thursday, then New Year’s Day will fall on a Thursday as well. What is the most recent year in which Christmas and New Year’s Day fell on different days of the week?
Utica College mathematician Hossein Behforooz devised this “permutation-free” magic square in 2007:
Each row, column, and long diagonal totals 2775, and this remains true if the digits within all 25 cells are permuted in the same way — for example, if we exchange the first two digits of each number, changing 231 to 321, etc., the square retains its magic sum of 2775. Further:
In 1945, the Arkansas legislature passed “An Act to Authorize and Permit Cities of First and Second Class and Incorporated Towns to Vacate Public Streets and Alleys in the Public Interest.” That seems boring enough. But § 8 read as follows:
“All laws and parts of laws, and particularly Act 311 of the Acts of 1941, are hereby repealed.”
With the stroke of a pen they had repealed every law in Arkansas. The state supreme court cleared its throat and ventured an improvement:
“No doubt the legislature meant to repeal all laws in conflict with that act, and, by error of the author or the typist, left out the usual words ‘in conflict herewith,’ which we will imply by necessary construction.”
(Act 17 of 1945 [repl. 1980; now Ark. Stat. § 14-301-301], cited in Antonin Scalia and Bryan Garner, Reading Law, 2012.)
I should have wished also to have referred to some of the serio-comic duels, such as that fought by the famous critic Sainte-Beuve against M. Dubois, of the Globe newspaper. When the adversaries arrived on the ground it was raining heavily. Sainte-Beuve had brought an umbrella and some sixteenth-century flint-lock pistols. When the signal to fire was about to be given, Sainte-Beuve still kept his umbrella open. The seconds protested, but Sainte-Beuve resisted, saying, ‘I am quite ready to be killed, but I do not wish to catch cold.’
— Theodore Child, “Duelling in Paris,” Harper’s New Monthly Magazine, March 1887
