# Catch as Catch Can

Claude Shannon, the father of information theory, took an active interest in juggling. He used to juggle balls while riding a unicycle through the halls of Bell Laboratories, and he built the first juggling robot from an Erector set in the 1970s. (The machine above mimics W.C. Fields, who himself juggled in vaudeville before turning to comedy.)

Noting that juggling seems to appeal to mathematics-minded people, Shannon offered the following theorem:

F is flight time, the time the ball spends in the air
D is “dwell time,” the time it spends in the hand
V is vacancy, the time a hand spends empty
B is the number of balls
H is the number of hands

“Theorem 1 allows one to calculate the range of possible periods (time between hand throws) for a given type of uniform juggle and a given time of flight,” he wrote. “A juggler can change this period, while keeping the height of his throws fixed, by increasing dwell time (to increase the period) or reducing dwell time to reduce the period. The total mathematical range available for a given flight time can be obtained by setting D = 0 for minimum range and V = 0 for maximum range in Theorem 1. The ratio of these two extremes is independent of the flight time and dependent only on the number of balls and hands.”

To measure dwell times, Shannon actually created a “jugglometer” in which a juggler wore copper mesh over his fingers and juggled foil-covered lacrosse balls; catching the ball closed a connection between the fingers and started a clock. “Preliminary results from testing a few jugglers indicate that, with ball juggling, vacant time is normally less than dwell time, V ranging in our measurements from fifty to seventy per cent of D.”

Shannon noted that juggling gets dramatically harder as the number of balls increases. He worked out a foolproof solution, at least in theory. A light ray that starts at one focus of an ellipse will be reflected to the other focus. If the ellipse is rotated around its major axis, it will create an egglike shell with two foci. Now if a juggler stands with a hand at each focus, then a ball thrown from either hand, in any direction, will bounce off the shell and arrive at the other hand!

(“Scientific Aspects of Juggling,” in Claude Elwood Shannon: Collected Papers, 1993.)

# Hooverball

Herbert Hoover weighed 200 pounds when he entered the White House in 1929. He couldn’t spare time for golf or tennis, so physician Joel Boone invented a game called Hooverball that could give him a strenuous workout in the minimum time.

On a tennis-like court, two teams of three players throw a 6-pound medicine ball back and forth over an 8-foot net. Sports Illustrated noted, “This cannot be accomplished graciously.” Rules:

1. The ball is served from the back line.
2. The ball must be caught in the air and immediately thrown back from the point where it was caught. It cannot be carried or passed.
3. Points are scored when a team fails to catch the ball, fails to throw it across the net, or throws the ball out of bounds.
4. A ball caught in the front half of one team’s court must be thrown to the back half of the opponents’ court. If it doesn’t reach the back court, the opponents score a point.
5. Scoring is exactly like tennis. The serve rotates among one team’s members until a game is won, then passes to the other team.
6. A ball that hits the line is good.
7. A player who catches the ball out of bounds can return to the court before throwing it back.
8. A ball that hits the net but passes over is a live ball.
9. Teams can make substitutions when the ball is dead.

Hoover played with his friends at 7 a.m. every day, even in snow. The regulars included the president, Boone, Supreme Court justices, Cabinet members, and journalists such as Mark Sullivan and William Hard. Talking shop was forbidden, and after the game they gathered on the White House lawn for juice and coffee.

“The regimen worked well for the president,” writes biographer Glen Jeansonn. “By the end of the term he had firmed up and slimmed down to 179 pounds. … Hoover looked forward to the games and the camaradarie, although he did not like rising quite so early. But the games were energizing and he began each day refreshed and relaxed.”

The Hoover Presidential Foundation, which co-hosts a national championship each year, has a complete set of rules.

# Small Wonder

Playing baseball for the St. Louis Browns, Eddie Gaedel had a career on-base percentage of 1.000, but most people have never heard of him.

Why? Because he had only one at-bat. Gaedel was a dwarf signed by the Browns as a publicity stunt in 1951. He had a legitimate contract, so the umpire had to let him play, but since he was only 3’7″, his strike zone measured an inch and a half.

“Three thoughts went through my mind that day,” said Frank Saucier, for whom Gaedel was pinch-hitting. “One, this is more like a carnival or a circus than a professional baseball game. Two, this is the greatest bit of showmanship I’ve ever seen. Three, this is the easiest money I’ll ever make.”

Tigers pitcher Bob Cain threw four balls, all high. The Tigers won 6-2, but Gaedel got a standing ovation. “For a minute,” he said, “I felt like Babe Ruth.” Today his jersey (number “1/8”) hangs in the Baseball Hall of Fame.

“He was, by golly, the best darn midget who ever played big-league ball,” wrote Browns owner Bill Veeck, who had cooked up the scheme. “He was also the only one.”

# In a Word

asmatographer
n. a composer of songs

While on the road with his 1927 musical Funny Face, George Gershwin left “two notebooks containing at least forty tunes” in a hotel room in Wilmington, Del. “After calling the hotel and learning the notebooks could not be located, he did not seem greatly perturbed,” wrote his brother and lyricist, Ira. “His attitude is that he can always write new ones.”

George was a songwriting machine, always at work. “I can think of no more nerve-wracking, no more mentally arduous task than making music,” he said in 1930. “There are times when a phrase of music will cost many hours of internal sweating.” Though he would sometimes try ideas at the piano, he insisted that “the actual composition must be done in the brain” — the fifth and final version of “Strike Up the Band” came to him in bed, and he heard, and even saw on paper, the complete construction of Rhapsody in Blue while riding a train from New York to Boston. “Like a pugilist,” he once said, “the songwriter must always keep in training.”

Ira’s struggle was less apparent. While working on lyrics he would wander the room, singing to himself or playing the piano with one finger. A new maid once asked his wife, “Don’t Mr. Gershwin never go to work?”

# Fiction and Feeling

A puzzle from University of Michigan philosopher Kendall Walton:

“Charles is watching a horror movie about a terrible green slime. He cringes in his seat as the slime oozes slowly but relentlessly over the earth, destroying everything in its path. Soon a greasy head emerges from the undulating mas, and two beady eyes fix on the camera. The slime, picking up speed, oozes on a new course straight toward the viewers. Charles emits a shriek and clutches desperately at his chair. Afterwards, still shaken, he confesses that he was ‘terrified’ of the slime.”

Was he? Walton says no. Charles may have felt intense fear, even shrieking as the slime approached the camera. But he knew that he was not literally in danger. This was not a half-belief or a “gut” feeling — he never considered leaving the theater or calling the police, for instance. Charles wasn’t motivated to avoid the slime physically. Yet he says that what he felt was fear of the slime.

What are we to make of this? “This issue is of fundamental importance,” Walton writes. “It is crucially related to the basic question of why and how fiction is important, why we find it valuable, why we do not dismiss novels, films, and plays as ‘mere fiction’ and hence unworthy of serious attention.” What is the answer?

(Kendall Walton, “Fearing Fictions,” Journal of Philosophy, January 1978.)

# Once for All

Asked to choose a single “master image” to sum up his work, Steven Spielberg chose this shot from Close Encounters, in which little Barry Guiler opens his living-room door to see the “beautiful but awful light” emanating from an alien spacecraft. “And he’s very small,” Spielberg said, “and it’s a very large door, and there’s a lot of promise or danger outside that door.”

The scene in which Barry encounters midnight visitors in his kitchen won praise for Spielberg’s direction of untrained 3-year-old actor Cary Guffey:

The story is recounted in Joseph McBride’s 2010 biography of Spielberg: “I had to the left of the camera a cardboard partition, and to the right of the camera a second cardboard partition. To the left of the camera, I put Bob Westmoreland, our makeup man, in a gorilla suit — the full mask and hands and hairy body. To the right of the camera, I dressed myself up as an Easter Bunny, with the ears and the nose and the whiskers painted on my face. Cary Guffey didn’t know what to expect. He didn’t know what he was gonna react to. His job was to come into the kitchen, stop at the door, and just have a good time. … And just as he came into the kitchen, I had the cardboard partition dropped and Bob Westmoreland was there as the gorilla. Cary froze, like a deer caught in car headlights … I dropped my partition, and he looked over at me, and there was the Easter Bunny smiling at him. He was torn. He began to smile at me — he was still afraid of that thing. Then I had Bob — I said, ‘Take off your head.’ Bob took off his mask, and when Cary saw it was the man that put his makeup on in the morning, Cary began to laugh. Even though it was a trick, the reaction was pure and honest.”

# Mob Rule

Eugene Graves and William Brown patented this grim game in 1902. A row of effigies stand on blocks under a gibbet. Each effigy is fitted with a noose, and the players take turns shooting balls at the blocks, “representing summary punishment meted out to the victim.”

In the patent abstract, the effigies are described only as “notorious criminals and persons opposed to law and order”; Graves and Brown note that these can be varied to suit the “location, place or country for which the game is especially designed.”

“A flag may be provided for each figure to designate the character or nationality of the effigy.” We’re lucky this didn’t catch on.

# Shop Talk

In 1869, composer Frederic Clay introduced W.S. Gilbert to Arthur Sullivan.

“I am very pleased to meet you, Mr. Sullivan,” said Gilbert, “because you will be able to settle a question which has just arisen between Mr. Clay and myself. My contention is that when a musician who is master of many instruments has a musical theme to express, he can express it as perfectly upon the simple tetrachord of Mercury (in which there are, as we all know, no diatonic intervals whatever) as upon the more elaborate disdiapason (with the familiar four tetrachords and the redundant note) which (I need not remind you) embraces in its simple consonance all the single, double, and inverted chords.”

This was gobbledegook that Gilbert had simply cooked up; he wanted to see whether it would “pass muster with a musician.”

Sullivan asked him to repeat the question, then politely said he would like to think it over before making a reply. In 1891 Gilbert said, “I believe he is still engaged in hammering it out.”

# STOP

When John Barrymore was on his deathbed in 1942, he received a wire from W.C. Fields.

It said YOU CAN’T DO THIS TO ME.

# “The Strangest Soccer Match Ever”

The football teams of Barbados and Grenada found themselves in a bizarre situation in a qualification round for the 1994 Carribean Cup. In order to advance to the finals, Barbados had to win this game by a margin of two goals; in any other outcome Grenada would qualify. Also, the tournament organizers had stated that if the teams reached a draw, extra time would be added to the match in which every goal would count double, the so-called “golden goal.”

Barbados was leading 2-0 when Grenada scored a goal in the final four minutes. With so little time remaining, the Barbados players conferred and, to everyone’s surprise, turned on their own goal, evening the score at 2-2. Their strategy was clear: If they could maintain this tie for the remaining few minutes, they’d be rewarded with an extra 30 minutes of playing time in which a single goal would give them the two-point margin they needed.

The Grenadians, realizing this, spent the last two minutes trying to get control of the ball and send it into their own goal — this would end the game at 3-2 and deny Barbados its two-goal margin.

The Barbadians, realizing this, began defending the Grenadian goal, effectively reversing the whole game. To add to the confusion, some Grenadians tried to make regular goals as well, which left Grenada attacking both goals, Barbados defending both, and most players and supporters utterly bewildered. The Barbadians eventually succeeded in holding the score at 2-2 — and made a winning goal in the extra time.

“I feel cheated,” complained Grenadian manager James Clarkson. “The person who came up with these rules must be a candidate for a madhouse. The game should never be played with so many players running around the field confused. Our players did not even know which direction to attack: our goal or their goal. I have never seen this happen before. In football, you are supposed to score against the opponents to win, not for them.” The Caribbean Cup retired the golden goal rule shortly thereafter.

(Thanks, Karl.)