Note

A poetic letter from Emily Dickinson to her aunt, Mrs. J. Howard Sweetser, late autumn 1884:

Dear Nellie,

I hardly dare tell you how beautiful your Home is, lest it dissuade you from the more mortal Homestead in which you now dwell — Each Tree a Scene from India, and Everglades of Rugs.

Is not ‘lead us not into Temptation’ an involuntary plea under circumstances so gorgeous? Your little note dropped in upon us as softly as the flake of Snow that followed it, as spacious and as stainless, a paragraph from Every Where — to which we never go — We miss you more this time, I think, than all the times before —

An enlarged ability for missing is perhaps a part of our better growth, as the strange Membranes of the Tree broaden out of sight.

I hope the Owl remembers me, and the Owl’s fair Keeper, indeed the remembrance of each of you, were a gallant boon — I still recall your Son’s singing, and when the ‘Choir invisible’ assemble in your Trees, shall reverently compare them — Thank you for all the Acts of Light which beautified a Summer now past to its reward.

Love for your Exile, when you write her, as for Love’s Aborigines — Our Coral Roof, though unbeheld, its foliage softly adds —

Emily, with Love

| Literature

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.)

| Science & Math

A Nonentity

In 1878 R.W.S. Ralston, assistant librarian of the British Museum, wrote to Leo Tolstoy asking for some biographical information for an article he was writing. Tolstoy wrote back:

Dear Sir,

I am very sorry not to be able to give you a satisfactory answer to your letter. The reason of it is that I very much doubt my being an author of such importance as to interest by the incidents of my life not only the Russian, but also the European public. I am fully convinced by many examples of writers, of whom their contemporaries made very much and which were quite forgotten in their lifetime, that for contemporaries it is impossible to judge rightly on the merits of literary works, and therefore, notwithstanding my wishes, I cannot partake the temporary illusion of some friends of mine, which seem to be sure that my works must occupy some place in the Russian literature. Quite sincerely not knowing if my works shall be read after a hundred years, or will be forgotten in a hundred days, I do not wish to take a ridiculous part in the very probable mistakes of my friends.

Hoping that on consideration of my motives you will kindly excuse my refusal,

I am yours faithfully,

Count L. Tolstoy

Ralston got the information from Turgenev. His article appeared in 1879 under the title “Count Leo Tolstoy’s Novels.”

| Literature

Progress

https://www.youtube.com/watch?v=dTd_M0gszvY

The clock on Bolivia’s congressional building runs counterclockwise.

Foreign Minister David Choquehuanca said the “clock of the south” had been adopted to affirm the country’s “southernness” and to encourage Bolivians to question norms and think creatively.

“Who says that the clock always has to turn one way?” he asked at a news conference in 2014. “Why do we always have to obey? Why can’t we be creative?”

Perhaps he’d been inspired by Venezuela, where in 2006 president Hugo Chávez raised a new national flag on which a white horse gallops left instead of right, “representing the return of Bolivar and his dream,” and the following year he put the nation’s clocks back half an hour “so that our bodies and above all our children take better advantage of sunlight and adapt the biological clock.”

| Oddities

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.)

| Science & Math

Strange Encounter

https://books.google.com/books?id=bcTE3-aFOlwC

In June 1867 French astronomer Camille Flammarion was floating west from Paris in a balloon when he entered a region of dense cloud:

Suddenly, whilst we are thus suspended in the misty air, we hear an admirable concert of instrumental music, which seems to come from the cloud itself and from a distance of a few yards only from us. Our eyes endeavour to penetrate the depths of white, homogeneous, nebulous matter which surrounds us in every direction. We listen with no little astonishment to the sounds of the mysterious orchestra.

The cloud’s high humidity had concentrated the sound of a band playing in a town square more than a kilometer below. Five years earlier, during his first ascent over Wolverhampton in July 1862, James Glaisher had heard “a band of music” playing at an elevation of nearly 4 kilometers (13,000 feet).

(From Glaisher’s Travels in the Air, 1871.)

| Oddities · Science & Math

A Problem From 1725

archimedes problem

Suppose that when Marcellus besieged Syracuse, Archimedes was standing at a corner of the city wall. A ditch runs parallel to the wall, separated from it by a distance a. To Archimedes’ left at distance b along the wall stands a catapult, which is distance c from a line perpendicular to the ditch. If Archimedes’ line of sight to the camp runs perpendicular to the wall and the ditch, show that he stood a distance ab/c from the camp.

Click for Answer
| Puzzles

Podcast Episode 235: Leon Festinger and the Alien Apocalypse

https://www.maxpixel.net/Spaceship-Cover-Alien-Weird-Ufo-1951536

In 1955, aliens from the planet Clarion contacted a Chicago housewife to warn her that the end of the world was imminent. Psychologist Leon Festinger saw this as a unique opportunity to test a new theory about human cognition. In this week’s episode of the Futility Closet podcast we’ll follow him inside a UFO religion as it approaches the apocalypse.

We’ll also try to determine when exactly LBJ became president and puzzle over some wet streets.

See full show notes …

| Podcast · Science & Math · Society

Scattered Stars

When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.

That’s Walt Whitman. In 2000, mathematician Mike Keith noted a similar idea in Psalm 19:1-6:

The heavens declare the glory of God;
And the firmament sheweth his handywork.
Day unto day uttereth speech,
And night unto night sheweth knowledge.
There is no speech nor language,
Where their voice is not heard.
Their line is gone out through all the earth,
And their words to the end of the world.
In them hath he set a tabernacle for the sun,
Which is as a bridegroom coming out of his chamber,
And rejoiceth as a strong man to run a race.
His going forth is from the end of the heaven,
And his circuit unto the ends of it:
And there is nothing hid from the heat thereof.

So he married them by rearranging the psalm’s letters:

When I had listened to the erudite astronomer,
When his high thoughts were arranged and charted before me,
When I was shown the length and breadth and height of it,
The Earth, the horned Moon, the chariot of fire,
The hundredth flight of the shuttle through heavyish air,
How soon, mysteriously, I became sad and sick,
Had to wander out, ousted, charging through the forest,
Joining the sure chaos here in a foreign heath,
Having forgotten the vocation of the learned man,
And in the mystic clearing, once more looked up
In perfect silence at the sermon in the stars.

(Michael Keith, “Anagramming the Bible,” Word Ways 33:3 [August 2000], 180-185.)

| Language · Poems

Rubik’s Clock

https://commons.wikimedia.org/wiki/File:Rubiks-clock.jpg

Hungarian sculptor and architect Ernő Rubik presented this puzzle in 1988; it was originally created by Christopher C. Wiggs and Christopher J. Taylor. The puzzle has two sides, with nine clocks on each side, and the goal is to set all the clocks to 12 o’clock simultaneously.

There are two ways to adjust the clocks. Turning a wheel at any of the four corners will adjust the clock at that corner on both sides of the puzzle. And turning a wheel will also adjust the three clocks adjacent to that corner on one side of the puzzle or the other; which side is determined by the four buttons surrounding the central clock.

So, for example, pressing the northwest button “in” and then turning the northwest wheel will adjust the northwestern quartet of clocks and the corresponding corner clock on the other side of the puzzle. Pulling the northwest button “out” and turning the same wheel will adjust the northwestern clock on the front of the puzzle, its counterpart on the back, and the three clocks adjacent to it on that side.

This is more intuitive than it sounds. Here’s a simulator.

Since there are 14 independent clocks, with 12 settings each, there are a total of 1214 = 1,283,918,464,548,864 possible configurations. It turns out that no configuration requires more than 12 moves to solve; for comparison, in the “worst case” solving a Rubik’s cube can take 20 moves. The trouble, of course, is knowing how to go about it.

| Puzzles · Science & Math