Diversion

https://archive.org/details/mad-43-man-squamish-mad-095/mode/2up

In 1965, Mad Magazine presented the rules of a deliberately incomprehensible sport. 43-Man Squamish was designed to be impossible to play, but a nameless Wikipedia editor has heroically summarized the rules:

Each team consists of one left and one right Inside Grouch, one left and one right Outside Grouch, four Deep Brooders, four Shallow Brooders, five Wicket Men, three Offensive Niblings, four Quarter-Frummerts, two Half-Frummerts, one Full-Frummert, two Overblats, two Underblats, nine Back-Up Finks, two Leapers and a Dummy—for a total of 43. The game officials are a Probate Judge (dressed as a British judge, with wig), a Field Representative (in a Scottish kilt), a Head Cockswain (in long overcoat), and a Baggage Smasher (dressed as a male beachgoer in pre–World War I years). None of the officials has any authority after play has begun.

Squamish is played on a pentagonal field, or Flutney, and the game is divided into a period of 15 minutes, known as an Ogre. Most squamish games consist of seven Ogres, unless of course, it rains. In that case, they are to play eight Ogres. Competitors wear gloves, a helmet, and flippers. They pursue the Pritz (or ball), which is 3 3/4 inches in diameter, constructed from untreated ibex hide, and is stuffed with blue jay feathers. Each player is equipped with a Frullip, a long hooked stick very similar in appearance to a shepherd’s crook that is used to impede opponents.

Before any game, the Probate Judge must first flip a coin, usually a new Spanish peseta, while the Visiting Captain guesses the toss. If he guesses correctly, the game is cancelled immediately. If not, the Home Team Captain must then decide if he wishes to play offense or defense first. Play begins after a frullip is touched to the flutney and the recitation “Mi tío es enfermo, pero la carretera es verde!”, a wise old Chilean saying that means, “My uncle is sick but the highway is green!” Penalties are applied for infractions such as walling the Pritz, icing on fifth snivel, running with the mob, rushing the season, inability to face facts, or sending the Dummy home early.

The offensive team has five Snivels to advance to the enemy goal. Carrying the Pritz across the goal line is a Woomik and scores 17 points; hitting it across with the frullip counts as a Durmish and only scores 11 points. Except in the 7th Ogre (and the 8th, if it rains), only the offensive Niblings and Overblats are allowed to score. In such cases, the four Quarter-Frummerts are allowed to kick or throw the Pritz, and the nine Finks are allowed to heckle the opposition by doing imitations of Barry Goldwater.

The teams must play a sudden-death overtime to break a tie, unless both Left Overblats are out of the game on personal fouls. If this is the case, the tie is settled by the teams lining up on opposite sides of the flutney (inherently difficult on a pentagonal shape) and shouting dirty limericks at each other until one side breaks up laughing.

When an insufficient number of players precludes a regulation 43-Man Squamish match, a simplified version may be played: 2-Man Squamish. The rules are identical, except in 2-Man Squamish, the object is to lose.

Writer Tom Koch had intended the game to be absurd, but several colleges fielded teams. Rensselaer Polytechnic issued a public challenge to Harvard; Marquette reported that its players had been suspended for “sportsmanlike conduct”; and the University of Alberta’s team boasted that “we happen to be the only undefeated Squamish team in Western Canada, mainly because we are the only team in Western Canada, and we haven’t played a game. We can’t understand why we have no opposition.”

In an ending that would have baffled the writer, Squamish is the highlight of Koch’s 2015 obituary in the New York Times, which credits him with a “vexingly convoluted game.”

The Sylvester–Gallai Theorem

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

Every finite set of points in the Euclidean plane that is not collinear has a line that passes through exactly two of the points.

This proof is by Michigan State University mathematician Leroy Milton Kelly. Consider a set S of points that aren’t all collinear, and define a connecting line to be a line that contains at least two of these points. There must be some point P and connecting line ℓ that are closer together than any other point-line pair in the set. Kelly now proves that ℓ contains only two of the points in S.

Assume that this isn’t true; that is, assume that ℓ contains more than two points in S. Then it passes through at least three points in the set. At least two of these must fall on the same side of P′, the perpendicular projection of P on ℓ. Call these two points B and C, with B being closest to P′. If we draw a connecting line 𝓂 that passes through P and C, and draw the perpendicular from B to B′ on 𝓂, then BB′ will be shorter than PP′ (because PP′C and BB′C are similar triangles).

This is a contradiction — we’d defined P and ℓ as the point-line pair that are closer together than any other pair in the set. So our assumption that ℓ contains more than two points can’t be true.

The Moral Superiority Illusion

In 2017, University of London psychologists Ben Tappin and Ryan McKay asked 270 subjects to evaluate both themselves and the average person as to traits describing morality (honest, trustworthy, fair), agency (hardworking, knowledgeable, competent), and sociability (cooperative, warm, family-orientated).

They found that nearly all the subjects inflated their own desirable moral qualities irrationally. The more desirable a moral trait appeared to the subjects, the more likely they were to ascribe it to themselves.

“The belief that one is morally superior to the average person appears robust and widespread,” they wrote. “We find that moral superiority represents a uniquely strong and prevalent instance of ‘positive illusion.'”

(Ben M. Tappin and Ryan T. McKay, “The Illusion of Moral Superiority,” Social Psychological and Personality Science 8:6 [August 2017], 623-631.)

The Tennis Racket Theorem

Experimenting in microgravity aboard the Mir space station in 1985, Soviet cosmonaut Vladimir Dzhanibekov watched a spinning wingnut flip spontaneously in midair. He was observing a phenomenon that had first been described mathematically by Louis Poinsot in 1834 — when a rigid body with three distinct principal moments of inertia is rotated around its intermediate axis, it can exhibit unpredictable 180-degree flips even in the absence of external torques.

This can be demonstrated easily with a tennis racket: When the racket is flipped around its first or third principal axis (the first and third images below), it doesn’t also undergo a half-rotation around another axis. But when it’s flipped around the intermediate axis (center image), it tends to contort itself so that it’s caught with the opposite face upward. (The racket in this demonstration is colored half white and half black to make this clearer.)

https://commons.wikimedia.org/wiki/File:Tennis_racket_theorem.gif
Image: Wikimedia Commons

Long Distance

de moraes chess puzzle

In this classic puzzle by Florencio Mendes de Moraes, White must checkmate Black in seven moves. The catch is that all three of his queens are confined to the leftmost file.

Either of two first moves will get things started, but beyond that there’s only one sequence that will work. What is it?

Click for Answer

Out of Joint

https://commons.wikimedia.org/wiki/File:2017-02_Raffaello_Sorbi_-_Time_on_his_hands.jpg

“A man of correct insight among those who are duped and deluded resembles one whose watch is right while all the clocks in the town give the wrong time. He alone knows the correct time, but of what use is this to him? The whole world is guided by the clocks that show the wrong time.” — Schopenhauer, Counsels and Maxims

A Wide Net

Entries in the index of Charles Cotton’s 1685 translation of Montaigne’s essays:

Ancient History how far respectable
Ants Conference
Arts taught to Men by other Animals
Books, immortal Children
Chearfulness Sign of Wisdom
Chewing accounted unbecoming
Clothes unknown to many Nations
Compositions that smell of Oil and the Lamp
Convenience, none without Inconvenience
Counsel’s Strength consists in Time
Desire of gathering Riches has no Limits
Dowry, great, Ruin of Families
Dying for Fear of Death
Elephant, discovering the Cheat of his Keeper
Feet performing the Service of Hands
Fortune often coincides with Reason
Foxes judging of the Thickness of the Ice by hearing
Goats trained up to give suck to Children
Greyhound’s Imagination
Head uncovered in the Presence of the Gods, why
Hedgehogs Foreknowledge of the Wind
Hospitals for Beasts
Kings and Coblers Souls cast in the same Mold
Lice cracked with the Teeth
Life, many Ways to get rid of it
Magpie that imitated the Trumpet
Monsters, whether there are such properly
Nations that sleep and wake by Half Years
Nobility, what
Opinion gives Weight and Value to Things
Parchment Scrolls tied about the Neck of Pericles
Parents dead Bodies eaten by their Children
Pedants despised
Pleasures wheedle and caress only to strangle us
Poverty obstinate
Prince ought to be himself in the Field
Revenge against inanimate Creatures
Skin of a Man, sufficient Proof against Weather
Trees buried in Winter
Utility, public, too dearly purchased
Women are more learned than Men in Love’s Business
Word of Men, their only Tye on one another
World a Looking-Glass and Book

The full index (in three volumes) is here, here, and here. It was added after Cotton’s death; I’m not sure who composed it.

Quinary

https://commons.wikimedia.org/wiki/File:Jan_Santini_Aichel_-_Zelen%C3%A1_Hora_ground_plan_2.jpg

When Saint John of Nepomuk was martyred, legend claims that five stars appeared above his head. So in 1721, when Czech architect Jan Santini Aichel designed a church to commemorate the Bohemian clergyman, he gave it a fivefold symmetry: The circular nave is surrounded by five pairs of columns and five oval domes alternating with ogival apses. The primary altar (one of five) bears five angels supporting a heavenly sphere decorated with five stars.

It’s beautiful even from above — the surrounding ring cloister is divided into 10 sections by five chapels and five gates:

https://commons.wikimedia.org/wiki/File:KLG_4953_CZ_-_%C5%BD%C4%8F%C3%A1r_nad_S%C3%A1zavou,_Wallfahrtskirche_Zelen%C3%A1_Hora.jpg
Image: Wikimedia Commons