Drawing Sounds

In a 1946 essay, Warner Brothers animator Chuck Jones presented two shapes:

jones drawing 1

These represent two nonsense words, tackety and goloomb. Which is which? Most people decide immediately that the shape on the left is tackety — even though that word has no meaning.

Similarly, one of these shapes is a bassoon, and one is a harp:

jones drawing 2

Here again, the correspondence seems obvious. “These are static examples of what are mostly static sounds,” Jones wrote. “The art of animation brings them to life, brings them fluidity and power; endows them, in short, with the qualities of music. The field of graphic symbols is a great but highly unexplored field. It will, I believe, prove an important one to the musician, and to any audience that is interested in satisfying the visual appetite, side by side with the auditory appetite.”

German-American psychologist Wolfgang Köhler had considered the same question in 1929. It’s been documented as “the bouba/kiki effect.”

(Chuck Jones, “Music and the Animated Cartoon,” Hollywood Quarterly 1:4 [1946], 364-370.)


During the 1974 English Amateur stroke play championship at the Moortown Golf Club in Leeds, businessman Nigel Denham’s approach shot on the 18th fairway struck a path in front of the clubhouse and bounced up the steps, through the open door, off a wall, and into the bar.

Denham was allowed inside, having first removed his golf shoes as required by the club. Local rules showed that the clubhouse was not out of bounds, so it followed that the ball lay within an obstruction from which no relief was available. He could move a chair or a table, but once this was done there was no interference with his stance or the intended area of his swing. He reasoned that he must play the ball as it lay.

So he opened the window and shot the ball neatly through it. It traveled 20 yards and finished 12 feet from the hole, to an ovation from the bar patrons. He even completed the subsequent putt for par.

“In the fulness of time the details of this daring stroke were conveyed to the Rules of Golf Committee at St Andrews for adjudication,” writes Peter Dobereiner in The Book of Golf Disasters. “The commitee ruled that Denham should have been penalized two strokes for opening the window. Chairs, tables, beer mats and sundry impediments could be cleared aside with impunity as movable obstructions but the window, as an integral part of the immovable obstruction of a clubhouse, should not have been moved.”

The clubhouse has since been declared out of bounds.



In May 2017, brothers Ollie and Harry Ferguson launched a plastic pirate ship, the Adventure, into the North Sea at Peterhead, Scotland. It carried a message asking anyone who found it to record their location and return it to the sea. After the ship had visited Denmark, Sweden, and Norway, the crew of a Norwegian ship volunteered to launch the Adventure in new waters, and on Nov. 8 released it 100 miles off the coast of Mauritania, hoping that it would cross the Atlantic westward to the Americas.

It nearly ran aground in the Cape Verde Islands but had made it past Barbados by mid-May. You can track its progress here.

(Via MetaFilter.)

The Right Stuff

Take any two rational numbers whose product is 2, and add 2 to each. The results are the legs of a right triangle with rational sides.

For example, 13/17 × 34/13 = 2. If we add 2 to each of these we get 47/17 and 60/13 or, clearing fractions, 611 and 1020. The hypotenuse is 1189.

Because (z + 2)2 + [(2/z) + 2]2 = [z + 2 + (2/z)]2, if z is rational, so are all three sides.

(R.S. Williamson, “A Formula for Rational Right-Angle Triangles,” Mathematical Gazette 37:322 [December 1953], 289-290, via Claudi Alsina and Roger B. Nelsen, Icons of Mathematics, 2011.)



I remember, many years ago, when my imagination was warm, and I happened to be in melancholy mood, it distressed me to think of going into a state of being in which Shakespeare’s poetry did not exist. A lady whom I then much admired, a very amiable woman, humored my fancy, and relieved me by saying, ‘The first thing you will meet in the other world will be an elegant copy of Shakespeare’s works presented to you.’ Dr. Johnson smiled benignantly at this, and did not appear to disapprove of the notion.

— James Boswell, Life of Samuel Johnson, 1791

A Trojan Cow


On the evening of July 7, 1969, guards at the Berlin Wall stopped a van headed out of East Berlin. It was carrying a life-size cow that the workmen said would be used in a display in West Berlin. Inside the cow the guards found 18-year-old Angelika B. of Karl-Marx-Stadt. Her fiancé in West Berlin had paid her two accomplices 5,000 DM to smuggle her out; if they’d been successful they’d have received twice that. All three were arrested, and the two helpers were sentenced to three years in prison for “subversive people trafficking.” Angelika was sentenced to 2 years 10 months but was later ransomed by West Germany.

Apparently the cow had been used twice before, successfully, to bring escapees to the West.


Once in a Lifetime

L.E. Dickson on why he’d spent a decade writing a 1,602-page history of number theory: “It fitted with my conviction that every person should aim to perform at some time in his life some serious useful work for which it is highly improbable that there will be any reward whatever other than his satisfaction therefrom.”

“Yes, that man has missed something who has never awakened in an anonymous bed beside a face he will never see again, and who has never left a brothel at sunrise feeling like throwing himself into the river out of pure disgust for life.” — Flaubert

In writing obituaries, “act on the theory that any man has had at least one interesting thing happen to him.” — William S. Maulsby, Getting the News, 1925

The Wooden Horse


British inventor Richard Lovell Edgeworth (1744-1817) could be stunningly imaginative:

I was riding one day in a country, that was enclosed by walls of an uncommon height; and upon its being asserted, that it would be impossible for a person to leap such walls, I offered for a wager to produce a wooden horse, that should carry me safely over the highest wall in the country. It struck me, that, if a machine were made with eight legs, four only of which should stand upon the ground at one time; if the remaining four were raised up into the body of the machine, and if this body were divided into two parts, sliding, or rather rolling on cylinders, one of the parts, and the legs belonging to it, might in two efforts be projected over the wall by a person in the machine; and the legs belonging to this part might be let down to the ground, and then the other half of the machine might have its legs drawn up, and be projected over the wall, and so on alternately. This idea by degrees developed itself in my mind, so as to make me perceive, that as one half of the machine was always a road for the other half, and that such a machine never rolled upon the ground, a carriage might be made, which should carry a road for itself. It is already certain, that a carriage moving on an iron rail-way may be drawn with a fourth part of the force requisite to draw it on a common road.

This seems to anticipate the caterpillar track, and the tank, in the 1760s. He worked on this idea for 40 years, making more than 100 working models and even patenting the principle. Finally he let the patent expire, as it just wasn’t possible with the technology that was available to him. But “I am still satisfied that it is feasible. The experience, which I have acquired by this industry, has overpaid me for the trifling disappointments I have met with; and I have gained far more in amusement, than I have lost by unsuccessful labor.”

(From his memoirs.)

In a Word

n. respects or compliments

adj. appropriate; suitable; proper; fit

n. thorough care or attention

adj. royal

At the Athens Olympics of 1896, American runner Thomas Curtis asked his French competitor Albin Lermusiaux why he was putting on white gloves before the start of the 100-meter race.

Lermusiaux said, “Because I am running in front of the king.”

Containing an Arc

arc puzzle

University of Illinois mathematician John Wetzel called this one of his favorite problems in geometry. Call a plane arc special if it has length 1 and lies on one side of the line through its end points. Prove that any special arc can be contained in an isosceles right triangle of hypotenuse 1.

Click for Answer