A Thorough Anagram

This is incredible. In 2005, mathematician Mike Keith took a 717-word section from the essay on Mount Fuji in Lafcadio Hearn’s 1898 Exotics and Retrospective and anagrammed it into nine 81-word poems, each inspired by an image from Hokusai’s famous series of landscape woodcuts, the Views of Mount Fuji.

That’s not the most impressive part. Each anagrammed poem can be arranged into a 9 × 9 square, with one word in each cell. Stacking the nine grids produces a 9 × 9 × 9 cube. Make two of these cubes, and then:

  • In Cube “D” (for Divisibility), assign each cell the number “1” if the sum of the letter values in the corresponding word (using A=1, B=2, C=3 etc.) is exactly divisible by 9, or “0” if it is not.
  • In Cube “L” (for Length), assign each cell the number “1” if its word has exactly nine letters, or “0” if it does not.

Replace each “1” cell with solid wood and each “0” cell with transparent glass. Now suspend the two cubes in a room and shine beams of light from the top and right onto Cube D and from the front and right onto Cube L:

mike keith anagram cubes

The shadows they cast form reasonable renderings of four Japanese kanji characters relevant to the anagram:

The red shadow is the symbol for fire.
The green shadow is the symbol for mountain.
Put together, these make the compound Kanji symbol (“fire-mountain”) for volcano.

The white shadow is the symbol for wealth, pronounced FU
The blue shadow is the symbol for samurai, pronounced JI
Put together, these make the compound word Fuji, the name of the mountain.

See Keith’s other anagrams, including a 211,000-word recasting of Moby-Dick.

A Pretty Puzzle

https://www.reddit.com/r/mathpuzzles/comments/as1rye/found_this_out_in_the_wild/

I don’t know who came up with this; I found it on r/mathpuzzles. What’s the area of the red region?

Click for Answer

Topology

https://commons.wikimedia.org/wiki/File:Bridge_29_Macclesfield_Canal.jpg
Image: Wikimedia Commons

Like the Tehachapi Loop, this is a beautiful solution to a nonverbal problem. When the towpath switches to the other side of a canal, how can you move your horse across the water without having to unhitch it from the boat it’s towing?

The answer is a roving bridge (this one is on the Macclesfield Canal in Cheshire). With two ramps, one a spiral, the horse passes through 360 degrees in crossing the canal, and the tow line never has to be unfastened.

A Bite

From the Royal Society of Chemistry’s Chemistry World blog: In 1955, when impish graduate student A.T. Wilson published a paper with his humorless but brilliant supervisor, Melvin Calvin, Wilson made a wager with a department secretary that he could sneak a picture of a man fishing into one of the paper’s diagrams. He won the wager — can you find the fisherman?

http://prospect.rsc.org/blogs/cw/2011/07/15/8170/

Plutchik’s Wheel of Emotions

https://commons.wikimedia.org/wiki/File:Plutchik-wheel.svg

In 1958 psychologist Robert Plutchik suggested that there are eight primary emotions: joy, sadness, anger, fear, trust, disgust, surprise, and anticipation. Each of the eight exists because it serves an adaptive role that gives it survival value — for example, fear inspires the fight-or-flight response.

He arranged them on a wheel to show their relationships, with similar emotions close together and opposites 180 degrees apart. Like colors, emotions can vary in intensity (joy might vary from serenity to ecstasy), and they can mix to form secondary emotions (submission is fear combined with trust, and awe is fear combined with surprise).

When all these combinations are included, the system catalogs 56 emotions at 1 intensity level. And in his final “structural model” of emotions, the petals are folded up in a third dimension to form a cone.

Dictum

https://commons.wikimedia.org/wiki/File:Pheasant_Shooting_-_Henry_Alken.png

Hunters of the 19th century defended their practice in part because it was the only way to identify species that would otherwise remain unknown.

They distilled this into an adage: “What’s hit is history, what’s missed is mystery.”

Art Appreciation

https://commons.wikimedia.org/wiki/File:African_Hooded_Vulture_(Necrosyrtes_monachus),_Kruger_National_Park.jpg
Image: Wikimedia Commons

In 1833, to show that vultures found their prey by sight rather than smell, naturalist John Bachman made “a coarse painting representing a sheep skinned and cut open”:

This proved very amusing — no sooner was this picture placed on the ground than the Vultures observed it, alighted near, walked over it, and some of them commenced tugging at the painting. They seemed much disappointed and surprised, and after having satisfied their curiosity, flew away. This experiment was repeated more than fifty times, with the same result.

He confirmed the result by setting the painting within two feet of a heap of camouflaged offal in his garden. “They came as usual, walked around it, but in no instance evinced the slightest symptoms of their having scented the offal which was so near them.” He concluded that, while vultures may have a sense of smell, they don’t use it to find food.

See Vulture Picnic.

Memory Limit

In 1956 Harvard psychologist George Miller pointed out a pattern he’d observed. If a person is trained to respond to a given pitch with a corresponding response, she’ll respond nearly perfectly when up to six pitches are involved, but beyond that her performance declines. Humans seem to have an “information channel capacity” of 2-3 bits of information: We can distinguish among 4-8 alternatives and respond appropriately, but beyond that number we start to founder.

A similar limit appears in studies of memory span. One psychologist read aloud lists of random items at a rate of one per second and then asked subjects to repeat what they’d heard. No matter what items had been read — words, letters, or numbers — people could store a maximum of about seven unrelated items at a time in their immediate memory.

It’s probably only a coincidence that these tasks have similar limits, but it’s still a useful rule of thumb: The number of objects an average person can hold in working memory is about seven.

(George A. Miller, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,” Psychological Review 63:2 [1956], 81-97.)

Pi Clacks

In 2003 mathematician Gregory Galperin of Eastern Illinois University offered a remarkable way to calculate π: Launch two masses toward an elastic wall, count the resulting collisions, and you can generate π to any precision, at least in principle.

“On the one hand, our method is purely mathematical and, most likely, will never be used as a practical way for finding approximations of π. On the other hand, this method is the simplest one among all the known methods (beginning from the ancient Greeks!).”

The video above, by 3Blue1Brown, gives the setup; the continuation is below. Via MetaFilter.

(Gregory Galperin, “Playing Pool With π (The Number π From a Billiard Point of View),” Regular and Chaotic Dynamics 8:4 [2003], 375-394.)