Sideways Music

It’s sometimes contended that time is one of four similar dimensions that make up a single manifold that we call spacetime. The four dimensions are orthogonal to one another, and though humans view one of them, time, as distinct from the others in various ways, it’s not intrinsically different.

Philosopher Ned Markosian offers a novel argument against this view: If aesthetic value is an intrinsic feature of an item, and if the four dimensions of spacetime are indeed similar, then rotating an object shouldn’t change its value. Turning a van Gogh painting 90 degrees doesn’t alter its beauty (though we may now have to turn our heads to appreciate it).

But turning a piece of music “out” of time, so that the notes of its melody, for example, occur all at once, changes the aesthetic value of the piece. “Whereas the original series of events had some considerable positive aesthetic value … the resulting series of events has either no aesthetic value or, more likely, negative aesthetic value. … Hence we have a powerful modus tollens argument against The Spacetime Thesis.”

(Ned Markosian, “Sideways Music,” Analysis 80:1 [January 2020], 51-59; and Sean Enda Power, Philosophy of Time: A Contemporary Introduction, 2021.)

| Art · Science & Math

Remembrance

The Fireside Book of Humorous Poetry contains this resonant scrap of anonymous verse:

John Wesley Gaines!
John Wesley Gaines!
Thou monumental mass of brains!
Come in, John Wesley
For it rains.

In The American Treasury, Clifton Fadiman writes, “Mr. Gaines is believed to have been a Congressman.” And lo, a John Wesley Gaines did indeed serve in the House, representing Tennessee’s 6th district from 1897 to 1909. A Washington journalist wrote in 1907, “Down in Tennessee they started a song about Gaines which found its way to Washington, and every now and then you’ll hear some one giving him a line of it just to liven things up a bit.”

Gaines is largely forgotten today, but I find that gimlet little rhyme in 18 different treasuries. I wonder who wrote it.

| History · Poems

Counting Up

A problem from Daniel J. Velleman and Stan Wagon’s excellent 2020 book Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles:

A square grid measures 999×999. Each square is either black or white. Each black square that’s not on the border of the grid has exactly five white squares among its eight immediate neighbors (those that adjoin it horizontally, vertically, or diagonally). Each white square that’s not on the border has exactly four black squares among its immediate neighbors. Of the 999 × 999 = 998001 squares in the grid, how many are black and how many white?

Click for Answer
| Puzzles

Visionary

Somebody said that it couldn’t be done —
But he, with a grin, replied
He’d never be one to say it couldn’t be done —
Leastways, not ’til he’d tried.
So he buckled right in, with a trace of a grin;
By golly, he went right to it.
He tackled The Thing That Couldn’t Be Done!
And he couldn’t do it.

— Anonymous

03/26/2024 This seems to be a reply to Edgar Albert Guest’s poem “It Couldn’t Be Done.” A couple of readers recognized it from The Dick Van Dyke Show (“The Return of Edwin Carp,” April 1964), but I don’t know whether that’s where it originated. (Thanks, Kevin, Chris, and Seth.)

| Poems

Specialist

A puzzle by Soviet science writer Yakov Perelman: Six carpenters and a cabinetmaker were hired to do a job. Each carpenter was paid 20 rubles, and the cabinetmaker was paid 3 rubles more than the average wage of the whole group. How much did the cabinetmaker make?

Click for Answer
| Puzzles

Flight

https://archive.org/details/sim_strand-magazine_july-december-1894_8/page/734/mode/2up?view=theater

In an article on secret hiding places in the Strand, December 1894, James Scott describes an ingenious refuge in the space between two matched flights of stairs. The functional set of risers on top can be raised to reveal a false set below, and the fugitive can take his place in the space between the two. When the door is closed again, searchers see only an ordinary staircase, and if they examine the empty cupboard beneath they’ll see only the apparent undersides of the risers above, which match them in number and size. There’s no perspective from which they can view the purported single stair from both above and below, and thus no reason to imagine that it might be double.

“Tapping upon what they believed to be the underside of the proper stairs would produce a hollow sound; but as a similar response must be expected when legitimate stairs are tapped, that point would not be considered a valuable clue,” Scott writes. “The quarters would be truly uncomfortable, as the necessities of the position would demand that the prisoner should lie at full length in the cavity. Perhaps, however, some provision was made whereby slight relief was afforded.”

| Oddities

Authority

https://commons.wikimedia.org/wiki/File:Paul_van_Somer_(c._1576-1621)_-_James_VI_%5E_I_(1566-1625)_-_RCIN_404446_-_Royal_Collection.jpg

“King James said to the fly, Have I three kingdoms, and thou must needs fly into my eye?” — John Selden

“The autocrat of Russia possesses more power than any other man in the earth, but he cannot stop a sneeze.” — Mark Twain

| Society

Mass Transit

A problem from the October 1964 issue of Eureka, the journal of the Cambridge University Mathematical Society:

The planet Kophikkup is in the shape of a torus or ring-doughnut. There is a direct mono-rail line from each of the four space-ports to each of the major cities. No lines join or cross. What is the greatest possible number of major cities? Draw a diagram for this case.

Click for Answer
| Puzzles

Anagram

Corresponding with Leibniz about his method of infinite series in 1677, Isaac Newton wanted to advert to his “fluxional method,” the calculus, without actually revealing it. So he used an unusual expedient — after describing his methods of tangents and handling maxima and minima, he added:

The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6accdae13eff7i3l9n4o4qrr4s8t12ux. On this foundation I have also tried to simplify the theories which concern the squaring of curves, and I have arrived at certain general Theorems.

That peculiar string is an inventory of the letters in the phrase that Newton wanted to conceal, Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa, which means “Given an equation involving any number of fluent quantities to find the fluxions, and vice versa.” So “6a” indicates that the Latin phrase contains six instances of the letter A, “cc” means that there are two Cs, and so on. In this way Newton could register his discovery without actually revealing it — the fact that he could present an accurate letter inventory of the fundamental theorem of the calculus proved that he’d established the theorem by that date. (More details here.)

Robert Hooke had used the same resource in 1660 to establish priority for his eponymous law before he was ready to publish it. And Galileo first published his discovery of the phases of Venus as an anagram. The technique today is known as trusted timestamping.

(Thanks, Andy.)

| Science & Math