Noted in Passing

In Visual Thinking in Mathematics, M. Giaquinto writes, “Calculus grew out of attempts to deal with quantitative physical problems which could not be solved by means of geometry and arithmetic alone. Many of these problems concern situations which are easy to visualize. In fact visual representations are so useful that most books on calculus are peppered with diagrams.” But there’s an intriguing footnote: “Moshé Machover brought to my attention a notable exception: Landau (1934). It has no diagram, and no geometrical application.”

That’s Differential and Integral Calculus, by Edmund Landau, a professor of mathematics at Gottingen University. Machover is right — the 366-page volume contains not a single diagram. Landau writes, “I have not included any geometric applications in this text. The reason therefor is not that I am not a geometer; I am familiar, to be sure, with the geometry involved. But the exposition of the axioms and of the elements of geometry — I know them well and like to give courses on them — requires a separate volume which would have to precede the present one. In my lecture courses on the calculus, the geometric applications do, of course, make up a considerable portion of the material that is covered. But I do not wish to wait any longer to make generally available an account, rigorous and complete in every particular, of that which I have considered in my courses to be the most suitable method of treating the differential and integral calculus.”

The book was quite successful — the first English edition appeared in 1950, and subsequent editions have continued right up through 2001.

His and Hers

russell illusion

Which of these faces is male, and which female? In fact both photos show the same androgynous face; the only difference is the amount of contrast in the image. But most people see the face on the left as female and the one on the right as male.

Gettysburg College psychologist Richard Russell says, “Though people are not consciously aware of the sex difference in contrast, they unconsciously use contrast as a cue to tell what sex a face is. We also use the amount of contrast in a face to judge how masculine or feminine the face is, which is related to how attractive we think it is.”

Cosmetics may serve to make a female face more attractive by heightening this contrast. “Cosmetics are typically used in precisely the correct way to exaggerate this difference,” Russell says. “Making the eyes and lips darker without changing the surrounding skin increases the facial contrast. Femininity and attractiveness are highly correlated, so making a face more feminine also makes it more attractive.”

(Richard Russell, “A Sex Difference in Facial Pigmentation and Its Exaggeration by Cosmetics,” Perception 38:8 [August 2009], 1211-1219.)


Artist Devorah Sperber plays with pixels. She renders an image at a low resolution and then replaces each element with a mass-produced object such as a spool of thread or a pipe cleaner. The results demonstrate how adeptly our brains recognize familiar images, even when given very little information.

She says, “As a visual artist, I cannot think of a topic more stimulating and yet so basic than the act of seeing — how the human brain makes sense of the visual world.”

There’s a gallery at her website.

Podcast Episode 160: The Birmingham Sewer Lion

Birmingham, England, faced a surprising crisis in 1889: A lion escaped a traveling menagerie and took up residence in the city’s sewers, terrifying the local population. In this week’s episode of the Futility Closet podcast we’ll descend into the tunnels with Frank Bostock, the 21-year-old manager who set out to capture the desperate beast.

We’ll also revisit a cosmic mystery and puzzle over an incomprehensible language.

See full show notes …

To Whom It May Concern

When Westinghouse buried a time capsule at the 1939 World’s Fair, the planners hoped that it wouldn’t be opened until 6939. That created a problem: How could they leave writings for a future civilization when language itself was sure to change immeasurably in the ensuing 5,000 years?

Westinghouse tried to solve the problem by enlisting Smithsonian ethnologist John P. Harrington, who wrote a “mouth map” (“Mauth Maep”) showing the pronunciation of “33 sounds of 1938 English” and a list of “the thousand words most essential to our daily speech and thought.” He also presented Aesop’s fable “The North Wind and the Sun” in “neo-phonetic spelling” and in 1938 English:

Dhj Northwind aend dhj Sjn wjr dispyucting whitsh woz dhj stronggjr, hwen j traevjljr kecm jlong raepd in j worm klock. Dhec jgricd dhaet dhj wjn huc fjrst mecd dhj traevjljr teck of hiz klock shud bic konsidjrd stronggjr dhaen dhj jdhjr. Dhen dhj Northwind bluc widh aol hiz mait, bjt dhj mocr hie bluc, dhj mocr klocsli did dhj traevjljr focld hiz klock jraund him, aend aet laest dhj Northwind gecv jp dhj jtempt. Dhen dhj Sjn shocn aut wormli, aend imicdijtli dhj traevjljr tuk of hiz klock; aend soc dhj Northwind woz jblaidzhd tj konfes dhaet dhj Sjn woz dhj stronggjr jv dhj tuc.

The Northwind and the Sun were disputing which was the stronger, when a traveler came along wrapped in a warm cloak. They agreed that the one who first made the traveler take off his cloak should be considered stronger than the other. Then the North wind blew with all his might, but the more he blew, the more closely did the traveler fold his cloak around him; and at last the Northwind gave up the attempt. Then the Sun shone out warmly, and immediately the traveler took off his cloak; and so the Northwind was obliged to confess that the Sun was the stronger of the two.

But even if the book manages to convey 20th-century vocabulary, grammar, and pronunciation to future scholars, will the world that these describe be too remote for them to imagine? The Westinghouse authors begged intermediate librarians to retranslate the book continually to keep alive its meaning. Will that be enough? I guess they’ll find out.

The Shoe Corner

shoe corner

This is interesting — one streetcorner in northwest Indiana abounds with discarded shoes. Somehow it’s become a tradition for people to leave unwanted footwear at 109th and Calumet Avenues in Hanover Township; the highway department removes the shoes periodically, but they keep accumulating.

“I have never seen anybody throw a shoe out there,” said St. John town manager Steve Kil, who can see the intersection from his house. “I just know that they’re always there.”

In 2009 the 86-year-old local historian told the Chicago Tribune that people had been dumping shoes at the corner for 50 years. Some mysterious clues: The pile is tallest on Monday mornings, and it grows fastest in the summer and dwindles by late August.

“I have to chuckle because I can remember when I was a child growing up in the 1970s, my mother would drive past this corner all the time,” Kil said. “She would slow down, and we would just examine the pile. And now I drive through here five days a week, and there’s always a new crop of shoes.”

Some locals call it the Corner of Lost Soles.

(Thanks, Andrew.)


In 1922 J.M. Barrie wrote to A.E. Housman:

Dear Professor Houseman,

I am sorry about last night, when I sat next to you and did not say a word. You must have thought I was a very rude man: I am really a very shy man.

Sincerely yours, J.M. Barrie

Housman wrote back:

Dear Sir James Barrie,

I am sorry about last night, when I sat next to you and did not say a word. You must have thought I was a very rude man: I am really a very shy man.

Sincerely yours, A.E. Housman

He added, “P.S. And now you’ve made it worse for you have spelt my name wrong.”

Higher Magic

The digits 1-9 can be arranged into a 3 × 3 magic square in essentially one way (not counting rotations or reflections) — the so-called lo shu square:

4    3    8

9    5    1

2    7    6

As in any magic square, each row, column, and diagonal produces the same total. But surprisingly (to me), the sum of the row products also equals the sum of the column products:

4 × 3 × 8 + 9 × 5 × 1 + 2 × 7 × 6 = 96 + 45 + 84 = 225

4 × 9 × 2 + 3 × 5 × 7 + 8 × 1 × 6 = 72 + 105 + 48 = 225

Even more surprisingly, the same is true of the Fibonacci sequence, if we arrange its first nine terms into a square array in the same pattern:

 3    2   21

34    5    1

 1   13    8

3 × 2 × 21 + 34 × 5 × 1 + 1 × 13 × 8 = 126 + 170 + 104 = 400

3 × 34 × 1 + 2 × 5 × 13 + 21 × 1 × 8 = 102 + 130 + 168 = 400

It turns out that this is true of any second-order linear recursion. (The sums won’t always be squares, though.)

From Edward J. Barbeau’s Power Play, 1997.


There is one very valid test by which we may separate genuine, if perverse and unbalanced, originality and revolt from mere impudent innovation and bluff. The man who really thinks he has an idea will always try to explain that idea. The charlatan who has no idea will always confine himself to explaining that it is much too subtle to be explained.

— G.K. Chesterton, Daily News, December 9, 1911