Blind Date

https://pixabay.com/en/clock-wall-clock-watch-time-old-1274699/

When I was 10 years old, a time machine appeared in my bedroom and my older self emerged and tried to kill me. He failed, of course, as his own existence must have shown him he would. But ever since I’ve wondered: This means that someday I myself must travel back to that bedroom and try to kill my younger self. And why would I ever do that?

This is not a logical or a metaphysical problem, but a psychological one. I can imagine being someday so depressed or ashamed or angry at myself that I’m motivated to travel back and try to erase my own existence. But I already know that the gun will jam. What earthly reason, then, could I have to go through the motions of a failed assassination? (Certainly we can imagine cases of amnesia, mistaken identity, etc., where such an action would make sense, but we’re interested in the basic straightforward case in which a time traveler interacts with his younger self — which surely would happen if time travel were possible.)

It seems that I must be motivated, somehow, in order for the appointment to take place, and yet the motivation seems to have no source. “In the present case, we have actions coming from nowhere, in the sense that no one decides, in the usual way, to perform them (or decides that they should be performed), and yet they are performed nonetheless,” writes University of Sydney philosopher Nicholas J.J. Smith. “The psychology of self-interaction is essentially different from that of interaction with others — because the former, but not the latter, involves the problem of agents knowing what they will decide to do, before they decide to do it.”

(Nicholas J.J. Smith, “Why Would Time Travelers Try to Kill Their Younger Selves?”, The Monist 88:3 [July 2005], 388-395.)

| Oddities

Going Places

Square wheels work fine if the road accommodates them — in this case, the road must be a series of catenaries suited to the size of the square. (A catenary is the shape that a cable assumes when suspended by its ends.)

Macalester College mathematician Stan Wagon designed a square-wheeled tricycle in 2004, and physics students at Texas A&M built a companion in 2007 (below).

| Science & Math

Podcast Episode 99: Notes and Queries

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In this week’s episode of the Futility Closet podcast we’ll take a tour through some oddities and unanswered questions from our research, including whether a spider saved Frederick the Great’s life, a statue with the wrong face, and a spectacularly disaster-prone oil tanker.

We’ll also revisit the lost soldiers of World War I and puzzle over some curiously lethal ship cargo.

See full show notes …

| Podcast

Magic Space

knecht most-perfect square

Craig Knecht, whose “terraformed” magic squares we explored in 2013, has begun to experiment with applying “magic” properties to David Hilbert’s space-filling curve.

The Hilbert curve finds its way to every cell in the square above by following the pattern shown at the lower left. Knecht divided that path into eight-cell segments, as shown in (a), and then sought solutions in which each colored eight-cell panel produced the magic sum of 260 while each of the eight ordinal positions across the eight panels did so as well. For example, in (b), a large red digit 1 marks the “first” position in each panel; the hope was to find values for these eight cells that would sum to 260, and likewise for all the “second” cells, the “third” ones, and so on.

The result, shown in (c), is a “most-perfect” magic square: Each colored panel sums to 260, and every set of cells that are 8 spaces apart on the Hilbert curve also sum to 260.

The next step was to apply this idea in three dimensions, and recently Knecht made the breakthrough shown below — a 4×4×4 “most perfect” number cube. The 64 numbers in the cube can be broken into 36 2×2 subsquares in each dimension, as shown. In all 108 of these subsquares, the four constituent numbers total 130. And as with the two-dimensional square above, a Hilbert curve can be drawn through the cube that visits each cell once, and cells that are eight cells apart on this curve sum to 260.

One of Knecht’s correspondents pointed out that the cube is even magicker than he had supposed: The “wraparound” subsquares (for example, 5, 28, 44, and 53 on the top of the cube) also sum to 130, as does each set of four corners, making a total of 192 2×2 subsquares that sum to 130.

“So in summary … making the Hilbert space-filling curve path have this magic property of values 8 spaces summing to the magic constant + this 2×2 planar criteria produces a very interesting cube!”

knecht most-perfect cube

| Science & Math

Black and White

spencer chess problem

G.B. Spencer devised this ingenious diagram in 1906: It contains 16 separate chess problems, one on each rank and file. In each case, ignore the pieces not on that rank or file and find a way for White to mate in two moves.

For example, the solution to the problem on the first rank is 1. Bd4 Ke2 2. Ng3#. What are the other 15 solutions?

Click for Answer
| Puzzles

Viewpoint

https://commons.wikimedia.org/wiki/File:Karl_D%C3%B6nitz.jpg

Captured by the British near the end of World War I, submarine commander Karl Dönitz was a prisoner at Gibraltar when news of the armistice came through. As he and a fellow German officer watched the celebrations “with infinitely bitter hearts,” a British captain joined them on deck.

Dönitz waved his arm in a gesture to encompass all the ships in the roads, British, American, French, Japanese, and asked if he could take any joy from a victory which could only be attained with the whole world for allies.

‘Yes,’ the Captain replied after a pause, ‘it’s very curious.’

In his memoirs, Dönitz wrote, “I will hold the memory of this fair and noble English sea officer in high regard all my life.”

(From Peter Padfield, Donitz: The Last Führer, 2013.)

| History

Parrot Talk

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At his death in 1880, Gustave Flaubert left behind notes for a Dictionary of Received Ideas, a list of the trite utterances that people repeat inevitably in conversation:

  • accident: Always “regrettable” or “unlucky” — as if a mishap might sometimes be a cause for rejoicing.
  • Archimedes: On hearing his name, shout “Eureka!” Or else: “Give me a fulcrum and I will move the world.” There is also Archimedes’ screw, but you are not expected to know what that is.
  • bachelors: All self-centered, all rakes. Should be taxed. Headed for a lonely old age.
  • book: Always too long, regardless of subject.
  • classics: You are supposed to know all about them.
  • forehead: Wide and bald, a sign of genius, or of self-confidence.
  • funny: Should be used on all occasions: “How funny!”
  • gibberish: Foreigners’ way of talking. Always make fun of the foreigner who murders French.
  • handwriting: A neat hand leads to the top. Undecipherable: a sign of deep science, e.g. doctors’ prescriptions.
  • jury: Do everything you can to get off it.
  • metaphors: Always too many in poems. Always too many in anybody’s writing.
  • original: Make fun of everything that is original, hate it, beat it down, annihilate it if you can.
  • pillow: Never use a pillow: it will make you into a hunchback.
  • restaurant: You should order the dishes not usually served at home. When uncertain, look at what others around you are eating.
  • taste: “What is simple is always in good taste.” Always say this to a woman who apologizes for the inadequacy of her dress.
  • war: Thunder against.
  • young gentleman: Always sowing wild oats; he is expected to do so. Astonishment when he doesn’t.

“All our trouble,” he wrote to George Sand, “comes from our gigantic ignorance. … When shall we get over empty speculation and accepted ideas? What should be studied is believed without discussion. Instead of examining, people pontificate.”

(Thanks, Macari.)

| Literature · Society

Unquote

pollock

“The love of complexity without reductionism makes art; the love of complexity with reductionism makes science.” — E.O. Wilson

| Quotations