In a Word

adj. musing, meditating, thoughtful, deep in thought

In his Treatise of the System of the World, Isaac Newton imagines firing cannonballs with greater and greater velocity from a high mountaintop. “The body projected with a less velocity, describes the lesser arc VD, and with a greater velocity, the greater arc VE, and augmenting the velocity, it goes farther and farther to F and G; if the velocity was still more and more augmented, it would reach at last quite beyond the circumference of the Earth, and return to the mountain from which it was projected.”

Indeed, if air resistance is not a factor, the cannonball will return to the mountain with the same velocity with which it left it, “and retaining the same velocity, it will describe the same curve over and over, by the same law,” like the moon. Thus with a simple thought experiment Newton conceived that gravity was the key force underlying planetary motion.

In a fitting tribute, the diagram above is now traveling beyond the solar system on the Voyager Golden Record, on a journey that its author helped to make possible.

Roaring Blazes

For his 1991 film Backdraft, director Ron Howard wanted fire to have a “brain,” like the shark in Jaws. So sound designer Gary Rydstrom added animal growls and howls to the sound of the flames. “You don’t hear them as animal sounds, but subconsciously it gives it an intelligence or a complexity it wouldn’t normally have.”

“For the suck in of air we used coyote howls. It wasn’t just a simple wind — it was more intelligent.”

“A lot of the fireball explosions were sweetened with monkey screams and different animal growls. Cougars make a great fire explosion sweetener. There’s a complexity to natural sounds, especially animal sounds, that is really wonderful.”

(From Vincent LoBrutto, Sound-on-Film, 1994.)

A Many-Sided Story


Back in September I posted a geometry problem mentioned by Andy Liu in Math Horizons in November 1997. Several readers recognized it and wrote in with the pretty solution — here it is:

As before, we’re given that ∠DCA = 20°, ∠ACB = 60°, ∠CBD = 50°, and ∠DBA = 30°, and we’re asked to find ∠CAD. Start by extending CD and BA to intersect at O, and draw a circle with O as the center and OB as the radius. Now, because ∠OCB and ∠OBC both measure 80°, BC is one side of an 18-gon inscribed in this circle.

Let E be the fifth vertex of this 18-gon to the left of C and F be the fifth vertex to the right of C. Also let G be the first vertex to the left of C and H be the first vertex to the right of B. Then, by symmetry, EB, GF, and OC meet. And by the central angle theorem ∠EBC is half the measure of ∠EOC, or 50°, so EB, GF, and OC meet at D.

Now, OFH is an equilateral triangle (by symmetry and the fact that ∠FOH is 60°), and ∠GFH is half the measure of ∠GOH, or 30° (again by the central angle theorem). So GF bisects OH.

Finally, by symmetry, AC = AH. But ∠ACD = 20° = ∠AOD, so triangle AOC is equilateral and AC = AO. Then AO = AH, and by symmetry AF bisects OH. And that means that GF passes through A.

Therefore, ∠BAD = ∠OAF, which is half of ∠OAH, or 70°. And from the information given at the start we can infer that ∠CAB = 40°. So ∠CAD = 30°.

I’m told that there are more problems like this in I.F. Sharygin’s 1988 book Problems in Plane Geometry. Thanks to the folks who wrote in about this.

11/06/2015 UPDATE: Another reader pointed out an alternate solution, discovered by Edward Mann Langley in 1922. (Thanks, January.)

“The Man in the Moon”

Phil Rizzuto’s digressive speaking style earned him a faithful following during his 40-year career as announcer for the New York Yankees. In 1993, Tom Peyer and Hart Seely found that the announcer’s disjointed speech worked exceptionally well as found poetry, and they edited a collection titled O Holy Cow! The Selected Verse of Phil Rizzuto. Here’s a sample: the announcer’s thoughts on the death of Yankees catcher Thurman Munson in an airplane crash:

The Yankees have had a traumatic four days.
Actually five days.
That terrible crash with Thurman Munson.
To go through all that agony,
And then today,
You and I along with the rest of the team
Flew to Canton for the services,
And the family …
Very upset.

You know, it might,
It might sound a little corny.
But we have the most beautiful full moon tonight.
And the crowd,
Enjoying whatever is going on right now.
They say it might sound corny,
But to me it’s like some kind of a,
Like an omen.

Both the moon and Thurman Munson,
Both ascending up into heaven.
I just can’t get it out of my mind.
I just saw the full moon,
And it just reminded me of Thurman Munson,
And that’s it.

Image: Wikimedia Commons

In 1726, the Swiss naturalist Johann Jakob Scheuchzer mistook the skull and vertebral column of a large salamander from the Miocene epoch for the “betrübten Beingerüst eines alten Sünders” (sad bony remains of an old human sinner) and dubbed it Homo diluvii testis, “the man who witnessed the Deluge.” The fossil lacked a tail or hind legs, so he thought it was the remains of a trampled human child:

It is certain that this [rock] contains the half, or nearly so, of the skeleton of a man; that the substance even of the bones, and, what is more, of the flesh and of parts still softer than the flesh, are there incorporated in the stone; in a word it is one of the rarest relics which we have of that accursed race which was buried under the waters. The figure shows us the contour of the frontal bone, the orbits with the openings which give passage to the great nerves of the fifth pair. We see there the remains of the brain, of the sphenoidal bone, of the roots of the nose, a notable fragment of the maxillary bone, and some vestiges of the liver.

The fossil made its way to Teylers Museum in the Netherlands, where in 1811 Georges Cuvier recognized it as a giant salamander. Ironically, Scheuchzer’s original belief is reflected in the fossil’s modern name, Andrias scheuchzeriAndrias means “image of man.”

Cutting Remarks

Until her death in 2010, film editor Sally Menke edited all of Quentin Tarantino’s films. He called Menke “hands-down my number one collaborator,” saying, “The best collaborations are the director-editor teams, where they can finish each other’s sentences.”

Because these films were edited in rented houses rather than in studio suites, Menke’s work was largely done alone. To keep her from getting lonely, Tarantino invited his cast and crew to address the camera between takes and say, “Hi, Sally!”

Reflected Glory

During a solar eclipse, the splashes of light that appear among the shadows of leaves take on the crescent shape of the sun.

In a pinch you can fashion your hands into a pinhole camera in order to observe an eclipse: Just make a loose fist of one hand and use it to focus the sun’s image onto the palm of your other hand. “The 0.25 cm (0.098 in) aperture f/200 optical system yields a reasonable image of the progress of the eclipse,” writes Peter L. Manly in Unusual Telescopes. “This telescope is easy to use, inexpensive and portable. The tracking system, however, leaves something to be desired.”

Podcast Episode 80: ‘Black Like Me’: Race Realities Under Jim Crow

john howard griffin

In 1959, Texas journalist John Howard Griffin darkened his skin and lived for six weeks as a black man in the segregated South. In this week’s episode of the Futility Closet podcast we’ll describe his harrowing experience and what it taught him about the true state of race relations in America.

We’ll also ponder crescent moons, German submarines, and griffins in India and puzzle over why a man would be arrested for winning a prize at a county fair.

Sources for our feature on John Howard Griffin:

John Howard Griffin, Black Like Me, 1961.

Robert Bonazzi, Man in the Mirror: John Howard Griffin and the Story of Black Like Me, 2010.

Maurice Dolbier, “Blinding Disguise in South,” Miami News, Oct. 15, 1961.

Jerome Weeks, “‘Black Like Me’ Just One of Many Roles for John Howard Griffin,” Dallas Morning News, Sept. 19, 1997.

H.W. Quick, “He Finds Bias Blighting North, South,” Milwaukee Sentinel, Jan. 16, 1964.

Karen De Witt, “Oppressor Shown What Being Oppressed Is Like,” Ottawa Citizen, Nov. 1, 1977.

Ray Sprigle, In the Land of Jim Crow, 1949.

Lucile Torkelson, “Writer Crosses the Race Barrier,” Milwaukee Sentinel, Oct. 29, 1969.

Research questions:

Here’s the image of the star and crescent:

And here are the sources I’ve found that describe the German submarine rescue:

Wolfgang Frank, The Sea Wolves, 1955.

Arch Whitehouse, Subs and Submariners, 1961.

Jacques Yves Cousteau, Captain Cousteau’s Underwater Treasury, 1959.

This week’s lateral thinking puzzle was contributed by listener Lawrence Miller.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at

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Many thanks to Doug Ross for the music in this episode.

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