Landscapes

Alexandra Kehayoglou makes carpets that evoke the topography of her native Argentina: grasslands, waterways, and glaciers. Her family opened a conventional carpet company there in 1956, and she discovered she could use scraps from their work to create “tactile canvases.” Each piece is composed by hand from discarded or surplus wool on a vertical frame, using a tufting gun and carpet scissors.

Her work often draws attention to natural areas altered by human activity in Argentina, such as the Raggio Creek north of Buenos Aires, destroyed for a shopping mall, or the Santa Cruz River, the last free-flowing wild river in the country, proposed site of two major hydroelectricity dams.

“It’s hard for people to understand that a rug can be art,” she told the New York Times. “But maybe that’s changing.”

More on her website, Facebook, and Instagram pages.

| Art

Chessametics

keith chessametic

Mike Keith published this remarkable invention in the Journal of Recreational Mathematics in 1975. Suppose a chess game goes:

P-K4   P-K4 
B-B4   P-R4 
Q-B3   P-R4 
QxP

This is checkmate, so White says “I win!” Now if the game score is written out in one column, including White’s exclamation:

P-K4
P-K4
B-B4
P-R4
Q-B3
P-R4
 QxP
----
IWIN

… we get a solvable alphametic — replace each letter (and the symbols x and -) with a unique digit and you get a valid sum. (The digits already shown count as numbers, and those numbers also remain available to replace letters.)

This example isn’t quite perfect — the two moves P-R4 are ambiguous, as is the final pawn capture. Keith’s Alphametics Page has an even better specimen, a pretty variation from a real 1912 game by Siegbert Tarrasch. It’s 13 moves long and forms a perfect alphametic with a unique solution.

| Puzzles

All Together Now

https://en.wikipedia.org/wiki/File:Front_page_of_Conlon_Nancarrow%27s_Study_for_Player_Piano_No._41.jpg

Because he wrote for player pianos, Conlon Nancarrow could demand more exacting performances than other composers. His Study No. 41 is in three parts for two pianos. The first canon has a time signature of \frac{1}{\sqrt{\pi}} / \sqrt{2/3} for the first piano; the second is in \frac{1}{3 \sqrt{\pi}} / \sqrt[3]{13/16} for the second piano; and the third is in \frac{\frac{1}{3 \sqrt{\pi}} / \sqrt[3]{13/16}}{\frac{1}{\sqrt{\pi}} / \sqrt{2/3}} for both pianos. In the third part, the two performances must be played in proportions marked in a diagram in the score (above). It sounds like this:

| Art

Podcast Episode 244: The Women’s Protest

https://commons.wikimedia.org/wiki/File:Rosenstrasse.jpg
Image: Wikimedia Commons

In February 1943, hundreds of German women joined in a spontaneous protest in central Berlin. They were objecting to the roundup of some of the city’s last Jews — their husbands. In this week’s episode of the Futility Closet podcast we’ll describe the Rosenstrasse protest, a remarkable example of civil disobedience.

We’ll also ponder whether a computer can make art and puzzle over some unusual phone calls.

See full show notes …

| History · Podcast · Society

Double Vision

French street artist JR has twice transformed I.M. Pei’s iconic pyramid at the Musée du Louvre in Paris.

In 2016 he made it disappear by overlaying one face with an image of the background facade.

And just this month (below) he applied 2,000 stickers to the surrounding pavement to create an anamorphic illusion in which the pyramid seems to rise from a crater.

The paper stickers were quickly destroyed by wandering tourists, but that was expected, he said. “The images, like life, are ephemeral. Once pasted, the art piece lives on its own. The sun dries the light glue and with every step, people tear pieces of the fragile paper. The process is all about participation of volunteers, visitors, and souvenir catchers.”

| Art

Cover Story

A set of points has diameter 1 if no two points in the set are more than 1 unit apart. An example is an equilateral triangle whose side has length 1. What’s the smallest shape that can cover any such set? A circle of diameter 1 won’t cover our triangle; part of the triangle projects beyond the circle:

https://commons.wikimedia.org/wiki/File:Lebesgue-circle-triangle.svg

Of course a larger circle would work, but what’s the smallest shape will always do the job? Surprisingly, no one knows. When French mathematician Henri Lebesgue posed the problem to Gyula Pál in 1914, Pál suggested a modified hexagon (in black):

https://commons.wikimedia.org/wiki/File:P%C3%A1l%27s_solution_to_Lebesgue%27s_universal_covering_problem.svg

Here Pál’s shape manages to surround a circle (blue), a Reuleaux triangle (red), and a square (green), each of diameter 1, and in fact it will accommodate any such set. Its own area is 0.84529946. Will a smaller shape do the job? Well, yes, but the gains get increasingly fine: In 1936 Roland Sprague whittled Pál’s shape down to 0.844137708436, and in 1992 H.C. Hansen reduced it further to 0.844137708398. At this point observers Victor Klee and Stanley Wagon wrote, “[I]t does seem safe to guess that progress on [this problem], which has been painfully slow in the past, may be even more painfully slow in the future.” But in 2015 John Baez reached 0.8441153 with an exquisite adjustment to two regions in Hansen’s shape; the smaller of these would span only a few atoms if the shape were drawn on paper.

Is that the end of the story? No: Last October Philip Gibbs claimed a further reduction to 0.8440935944, and the search goes on. In 2005 Peter Brass and Mehrbod Sharifi showed that the universal cover must have an area of at least 0.832, so there’s room, at least in theory, for still further improvements.

(Thanks, Jacob.)

| Science & Math

Wind Art

Anthony Howe creates wind-driven sculptures that somehow evoke both marine biology and alien machines.

“I attempt, with an economy of means, to construct objects whose visual references range from lo-tech sci-fi paraphernalia to microbiological or astronomical models,” he says. “Utilizing primarily stainless steel armatures that are driven either by hammered curvilinear shapes or flat fiberglass covered discs, I hope the pieces assume a spare, linear elegance when conditions are still, mutating to raucous animation when the wind picks up.”

More at his YouTube channel.

https://www.youtube.com/watch?v=J4l5rHNSq9s

| Art

Spine Tinglers

In a 2009 study of responses to music, neuroscientist Valorie Salimpoor and her colleagues asked participants to bring in 3 to 5 pieces of “intensely pleasurable instrumental music to which they experience chills.” Then they measured their physiological response as they listened. They found that the “chills” effect is real — when the subjects reported that their pleasure at the music was highest, so was their sympathetic nervous system activity, a measure of emotional arousal.

One byproduct of the study is a list of more than 200 chills-inducing moments in music of various genres, with precise timestamps of the crucial points:

Composer/Artist Title Chills
Beethoven Piano Sonata No. 17 in D Minor (“The Tempest”) 5:33
Mahler Symphony No. 1 – Movement 4 5:42, 9:57, 15:15
Charles Mingus Fables of Faubus 0:20, 7:10
Stan Getz Round Midnight 1:26
Pink Floyd Shine on You Crazy Diamond 5:00
Phish You Enjoy Myself 10:50
Cannonball Adderley One for Daddy-O 0:40
Los Angeles Guitar Quartet Congan 2:09
Crowfoot Larks in May 0:10, 2:00
Howard Shore The Breaking of the Fellowship (film score) 0:10, 0:55
Dave Matthews Band #34 1:40
The Dissociatives Paris Circa 2007 Slash 08 1:30
Brad Mehldau Knives Out 4:45, 7:25
Explosions in the Sky First Breath After Coma 2:25, 3:30, 8:10

These won’t work for everyone — music tastes are notoriously idiosyncratic — but it’s interesting to see what people find moving. The full list is here (Table_S1). (Note too that the timestamps relate to a particular recording, so consider them approximate in e.g. classical music.)

(Valorie N. Salimpoor, et al., “The Rewarding Aspects of Music Listening Are Related to Degree of Emotional Arousal,” PloS One 4:10 [2009], e7487.)

| Art · Science & Math