Command Performance

This mechanism, recently restored by Michael Start of the House of Automata, was probably fashioned by Blaise Bontems in Paris around 1890.

It’s an example of a lost art, the “singing bird box,” an early variety of automaton introduced by Pierre Jaquet-Droz in Geneva in 1784. The song is produced by a bellows, a whistle, and a system of cams; many of these devices added a mechanical bird that would flap its wings and open and shut its beak while the sound was produced.

Jaquet-Droz also created a stunning mechanical boy who writes custom texts with a quill pen; that unit, which still works, is made up of some 6,000 pieces.

A Near Miss

For a moment in the 1998 Simpsons episode “The Wizard of Evergreen Terrace,” it appears that Homer has found a solution to Fermat’s last theorem:

398712 + 436512 = 447212

If you check this on a calculator with a 10-digit display, it seems to work: Raise 3987 and 4365 each to the 12th power, take the 12th root of the sum, and you get 4472.

But that’s the fault of the display. The actual value for the third term is closer to 4472.000000007057617187512.

Simpsons writer David S. Cohen, who had studied physics at Harvard and contrived the ruse, told Simon Singh he was pleased at the consternation it caused online. “I feel great about it. It’s very easy working in television to not feel good about what you do on the grounds that you’re causing the collapse of society. So, when we get the opportunity to raise the level of discussion — particularly to glorify mathematics — it cancels out those days when I’ve been writing those bodily function jokes.”

(From Simon Singh, The Simpsons and Their Mathematical Secrets, 2013.)

Podcast Episode 327: The Misplaced Tourist,_Bangor,_Maine_(67541).jpg

In 1977, West German tourist Erwin Kreuz spent three days enjoying the sights, sounds, and hospitality of Bangor, Maine. Unfortunately, he thought he was in San Francisco, on the other side of the continent. In this week’s episode of the Futility Closet podcast, we’ll describe Kreuz’s unlikely adventure, which made him a local hero in his adopted city.

We’ll also consider an invisible killer and puzzle over a momentous measurement.

See full show notes …

“Problem for Poultry Farmers”

Eureka, the esteemed journal of recreational mathematics published at Cambridge University, has placed its archives online under a Creative Commons license. Here’s a problem from May 1940:

The chicken was twice as old when when the day before yesterday was to-morrow to-day was as far from Sunday as to-day will be when the day after to-morrow is yesterday as it was when when to-morrow will be to-day when the day before yesterday is to-morrow yesterday will be as far from Thursday as yesterday was when to-morrow was to-day when the day after to-morrow was yesterday. On what day was the chicken hatched out?

Click for Answer

Child’s Play

In 2002 a 7-year-old boy, Steven Olson, patented a “method of swinging on a swing”:

The method comprises the steps of: a) positioning a user on the seat; and b) having the user pull alternately on one chain to induce movement of the user and the swing toward one side, and then on the other chain to induce movement of the user and the swing toward the other side, to create side-to-side motion.

Steven’s father, Peter, a patent attorney, wanted to show him how the system works. Steven’s submission was approved at first (the patent office said that its technical definition of obviousness “is not necessarily the conventional definition”) but later reconsidered and invalidated, perhaps due to criticism.

A year earlier, to test the workability of a new national patent system, an Australian man had patented the wheel.

Vanishing Act

There is often peculiar humour about self-frustration. Consider, for example, a train of events which started outside the old Clarendon Laboratory, Oxford. I came across a dirty beaker full of water just when I happened to have a pistol in my hand. Almost without thinking I fired, and was surprised at the spectacular way in which the beaker disappeared. I had, of course, fired at beakers before; but they had merely broken, and not shattered into small fragments. Following Rutherford’s precept I repeated the experiment and obtained the same result: it was the presence of the water which caused the difference in behavior. Years later, after the War, I found myself having to lecture to a large elementary class at Aberdeen, teaching hydrostatics ab initio. Right at the beginning came the definitions — a gas having little resistance to change of volume but a liquid having great resistance. I thought that I would drive the definitions home by repeating for the class my experiments with the pistol, for one can look at them from the point of view of the beaker, thus suddenly challenged to accommodate not only the liquid that it held before the bullet entered it, but also the bullet. It cannot accommodate the extra volume with the speed demanded, and so it shatters.

— R.V. Jones, “Impotence and Achievement in Physics and Technology,” Nature 207:4993 (1965), 120-125

(When the Royal Engineers tried to use this trick to demolish a tall chimney, filling its base with 6 feet of water and firing an explosive charge into the water, “it succeeded so well that it failed completely”: The incompressible water flung the surrounding ring of bricks outward, leaving a foreshortened chimney suspended above in midair. This dropped down neatly onto the old foundation, upright and intact, “presenting the Sappers with an exquisite problem.”)

A Special Year

Reader Alan Jackson points out that 2021 is the product of consecutive primes: 2021 = 43 × 47.

It’s the first time this has happened since 1763 (= 41 × 43), and it won’t happen again until 2491 (= 47 × 53).

A quick way to find the factors is to note that 2021 is the difference of two squares, 452 – 22, so 2021 = (45 – 2) × (45 + 2).

(Thanks, Alan.)

Small World,_Kyiv.jpg
Image: Wikimedia Commons

In Antoine de Saint-Exupéry’s 1943 novella The Little Prince, the narrator encounters “a most extraordinary small person” whose planet is “scarcely any larger than a house.”

This led University of Ljubljana physicist Janez Strnad to consider the implications. If the radius of the prince’s planet were 64 meters and it had Earth’s density, then the weight of a prince with a mass of 30 kg would amount to 0.003 newtons, corresponding on Earth to the weight of a mass of 0.3 g. (If the planet had the density of an asteroid, his weight would be lower still.)

The planet cannot have an atmosphere, because the mean velocity of gas molecules is greater than the escape velocity.

If the prince moved faster than 80 millimeters per second he’d be sent into orbit around the planet; if faster than 11 centimeters per second he’d leave it altogether.

“He could overcome the limitations concerning his velocity by either binding himself with a rope to his planet or building a spherical shell around it,” Strnad concluded. “The human body adapts to weightlessness and astronauts have to perform special gymnastic exercises not to suffer on returning to the Earth. For the little prince, coming to Earth would be a serious adventure, were he not a fictitious character.”

(Janez Strnad, “The Planet of the Little Prince,” Physics Education 23:4 [1988], 224.)