Dedication

In the climactic scene that Ray Harryhausen animated for Jason and the Argonauts (1963), “I had three men fighting seven skeletons, and each skeleton had five appendages to move in each separate frame of film. This meant at least thirty-five animation movements, each synchronized to the actor’s movements. Some days I was producing just 13 or 14 frames a day, or to put it another way, less than one second of screen time per day, and in the end the whole sequence took a record four and a half months to capture on film.”

An interesting philosophical question: “So how do you kill skeletons? We puzzled over this conundrum for some time and in the end we opted for simplicity by having Jason jump off the cliff into the sea, followed by the skeletons. It was the only way to kill off something that was already dead, and besides, we assumed that they couldn’t swim. After filming a stuntman jump into the sea, the prop men threw seven plaster skeletons off the cliff, which had to be done correctly on the first take as we couldn’t retrieve them for a second. To this day there are, somewhere in the sea near that hotel on the cliff edge, the plaster bones of seven skeletons.”

(Ray Harryhausen: An Animated Life, 2010.)

| Entertainment

“Piccadilly Underground Station”

This unusual puzzle by G.A. Roberts appeared in the January 1941 issue of Eureka, the journal of recreational mathematics published at Cambridge University. It concerns the Piccadilly Circus station of the London Underground, which lies on the Piccadilly line between Green Park and Leicester Square and on the Bakerloo line between Charing Cross and Oxford Circus.

At a given time there are on the platform, escalators and subways, and in the trains, 128 people, all of whom travel by train, and none of whom return immediately by the way they have come.

Those who have come via Leicester Square are equal in number to those who are about to travel via Leicester Square.

The number of people who arrived by Bakerloo Line is equal to the number who intend to leave by the Piccadilly Line.

The number of people who are travelling from the street to stations on the Piccadilly Line is equal to six-thirteenths of the number who change from the Piccadilly Line to the Bakerloo.

The number who arrive from Green Park and then change to the Bakerloo is equal to the number who are about to travel via Green Park.

The number who are travelling from the street to the Bakerloo is equal to four times the number who arrive in Piccadilly trains but do not use the Bakerloo Line, and of these, twice as many come from Green Park as from Leicester Square.

By how many does the number of people who use the Bakerloo Line exceed that of those who do not?

Click for Answer
| Puzzles

Engine Trouble

In John Milton’s 1637’s poem “Lycidas,” corrupt clergy are threatened with a obscure punishment:

The hungry Sheep look up, and are not fed,
But swoln with wind, and the rank mist they draw,
Rot inwardly, and foul contagion spread:
Besides what the grim Woolf with privy paw
Daily devours apace, and nothing sed,
But that two-handed engine at the door,
Stands ready to smite once, and smite no more.

What is the “two-handed engine”? That’s been a riddle for nearly 400 years. In 1950, Oberlin College philologist W. Arthur Turner collected 10 possibilities, ranging from the nations England and Scotland to “[t]he sheep-hook, which in Milton’s day apparently had an iron spud on the straight end and could be used as a weapon.” Turner himself thought that “the only engine which does meet all the requirements is the lock on St. Peter’s door (or the power of the lock), to which he carries the key.” But there’s still no strong consensus.

(W. Arthur Turner, “Milton’s Two-Handed Engine,” Journal of English and Germanic Philology 49:4 [October 1950], 562-565.)

| Literature · Poems · Religion

“A Bully Is Always a Coward”

English proverbs:

  • Give neither counsel nor salt till you are asked for it.
  • A hedge between keeps friendship green.
  • A fault confessed is half redressed.
  • A hungry man is an angry man.
  • Please your eye and plague your heart.
  • If you run after two hares you will catch neither.
  • A good lawyer makes a bad neighbor.
  • Speak fair and think what you will.
  • It is not the suffering but the cause which makes a martyr.
  • A fool will laugh when he is drowning.
  • A foe is better than a dissembling friend.
  • A disease known is half cured.
  • Let your purse be your master.
  • Short counsel is good counsel.

And “Whosoever draws his sword against the prince must throw the scabbard away.”

| Quotations

Fitting

https://commons.wikimedia.org/wiki/File:Benoit_Mandelbrot_mg_1804c.jpg
Image: Wikimedia Commons

What does the middle initial “B.” stand for in Benoit B. Mandelbrot’s name?

Benoit B. Mandelbrot.

In the Notices of the American Mathematical Society, Andrew Kern calls this “My single favorite math joke of all.”

(Intriguingly, Mandelbrot adopted his middle initial; it does not stand for a middle name.)

03/02/2021 UPDATE: Reader Dan Uznanski sent another:

What’s an anagram for Banach-Tarski?

Banach-Tarski Banach-Tarski.

| Humor · Science & Math

Astrobiology

https://www.metmuseum.org/art/collection/search/811200

In 1776, draftsman Filippo Morghen produced a set of 10 etchings with a startling title: The Suite of the Most Notable Things Seen by Cavaliere Wild Scull, and by Signore de la Hire on Their Famous Voyage From the Earth to the Moon.

Philippe de La Hire was a real French astronomer; nothing is known of Scull, and in the second printing Morghen replaced him with natural philosopher Bishop John Wilkins as a putative source of his fantastic images.

As to life on the moon, it’s pretty wild — among other things, the lunar inhabitants live in pumpkins to protect themselves from wild beasts. You can see the whole series at Public Domain Review.

| Art · Oddities

Trying

I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now. I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different. Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

Try the experiment, and if you do not find it as I say, you are a mere sciolist, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

— Maria Price La Touche, The Letters of a Noble Woman, 1908

| Science & Math

Reflection

https://commons.wikimedia.org/wiki/File:08608_einstein_1916.jpg

In 1927 Albert Einstein sent a photograph of himself to his friend Cornelia Wolf. He inscribed these lines:

Wherever I go and wherever I stay,
There’s always a picture of me on display.
On top of the desk, or out in the hall,
Tied round a neck, or hung on the wall.

Women and men, they play a strange game,
Asking, beseeching: “Please sign your name.”
From the erudite fellow they brook not a quibble,
But firmly insist on a piece of his scribble.

Sometimes, surrounded by all this good cheer,
I’m puzzled by some of the things that I hear,
And wonder, my mind for a moment not hazy,
If I and not they could really be crazy.

| Poems · Science & Math · Society

Beholder

https://commons.wikimedia.org/wiki/File:Mona_Lisa,_by_Leonardo_da_Vinci,_from_C2RMF_retouched.jpg

New York Times, Dec. 1, 1913:

“In a lecture on ‘Beauty and Morality,’ at the University of London, one Kane S. Smith called the ‘Mona Lisa’ of Leonardo da Vinci ‘one of the most actively evil pictures ever painted, the embodiment of all evil the painter could imagine put into the most attractive form he could devise.'”

Literary Digest, Jan. 3, 1914:

“The lecturer admitted that it was an exquisite piece of painting, but said, ‘if you look at it long enough to get into its atmosphere, I think you will be glad to escape from its influence. It has an atmosphere of indefinable evil.'”

“The audience is stated to have applauded enthusiastically, but it is probable they would have applauded equally as heartily if the lecturer had found the influences of the picture good.”

| Art

Asked and Answered

In 1865, while conducting the “Answers to Correspondents” column in The Californian, Mark Twain received this inquiry:

If it would take a cannon ball 3 1/3 seconds to travel four miles, and 3 3/8 seconds to travel the next four, and 3 5/8 to travel the next four, and if its rate of progress continued to diminish in the same ratio, how long would it take it to go fifteen hundred millions of miles?

He responded:

I don’t know.

In a 1906 address to the New York Association for Promoting the Interests of the Blind, he said, “I never could do anything with figures, never had any talent for mathematics, never accomplished anything in my efforts at that rugged study, and today the only mathematics I know is multiplication, and the minute I get away up in that, as soon as I reach nine times seven … [Mr. Clemens lapsed into deep thought for a moment.] I’ve got it now. It’s eighty-four.”

| Literature · Science & Math