Black and White

penrose chess problem

Physicist Roger Penrose devised this problem in 2017 to illustrate the difference between artificial and human intelligence. James Tagg, leader of the Penrose Institute, told the Telegraph, “A human looking at it for a short while will ‘see’ what white must, and more particularly, must not do, and use very little energy to decide this. But, for a computer, the puzzle requires an enormous number of calculations, far too many for even today’s supercomputers.” What is White’s insight?

Click for Answer

Podcast Episode 318: Peace Pilgrim

peace pilgrim

In 1953 Mildred Norman renounced “an empty life of money and things” and dedicated herself to promoting peace. She spent the next three decades walking through the United States to spread a message of simplicity and harmony. In this week’s episode of the Futility Closet podcast we’ll describe her unusual life as a peace pilgrim.

We’ll also admire Wellington’s Mittens and puzzle over a barren Christmas.


In 1956, Navy pilot Tom Attridge overtook his own rounds in a supersonic jet.

Flemish artist Cornelius Gijsbrechts painted a rendering of the back of a painting.

See full show notes …

Hoary-Headed Frosts

The 2019/2020 Takhini Hot Springs Hair Freezing Contest attracted 288 contestants to the natural hot springs north of Whitehorse, Yukon. Air temperatures below -20°C will freeze all wet hair, including eyebrows and eyelashes — entrants ring a bell near the pool entrance to summon staff to take a photo, and then judges choose among the season’s entries.

Each winner gets $2,000.

In the Beginning

What was God doing before he made heaven and earth? … if (God) did nothing, why did he not continue in this way … forever … ? If any new motion arise in God, or a new will is formed in him, to the end of establishing creation which he had never established previously … then (God) is not truly … eternal. Yet if it were God’s sempiternal will for the creature to exist, why is not the creature sempiternal also?

— Augustine, Confessions

Wishful Thinking

In the 1850s, when a plague of spirits began to rotate tables at London séances, Michael Faraday devised a clever way to investigate: Two boards were lain one atop the other, with an upright haystalk inserted through the pair. The experimenters laid their hands on this. The apparatus gave a way to see “whether the table moved the hand, or the hand moved the table”: If the medium willed the table to move to the left, and it did so on its own, the haystalk would be seen to lean in one direction … but if the experimenters, even unconsciously, themselves pressed the table to turn, it would lean in the other.

Faraday wrote, “As soon as the index is placed before the most earnest, and they perceive — as in my presence they have always done — that it tells truly whether they are pressing downwards only or obliquely, then all effects of table-turning cease, even though the parties persevere, earnestly desiring motion, till they become weary and worn out. No prompting or checking of the hands is needed — the power is gone; and this only because the parties are made conscious of what they are really doing mechanically, and so are unable unwittingly to deceive themselves.”

(Michael Faraday, “On Table-Turning,” Times, June 30, 1853.)

More Reversible Verse

A followup to David L. Stephens’ palindromic poem “Hannibal, Missouri”: In Walt Kelly’s I Go Pogo (1952), some of the swamp critters are trying to find the turtle Churchy LaFemme guilty of something so they can have turtle soup. Deacon Mushrat announces, “Finally we have a cryptic bit written by Turtle that reeks of guilt”:

Smile, wavering wings
Above rains pour,
While hopefully sings
Love of shorn shore
Shore shorn of love
Sings hopefully while
Pour rains above,
Wings wavering, smile.

Miz Beaver says, “I don’t git it.”

Wiley Catt answers, “That’s the clever part. It’s gotta be read backward.”

(Thanks, Cleve.)


This was in the Public Domain Review yesterday — in 1917 the National Woman Suffrage Association published a little book purporting to give every reason women shouldn’t be given the franchise. Inside, every page page was blank.

The 19th amendment passed three years later. “Men and women are like right and left hands,” wrote Jeannette Rankin. “It doesn’t make sense not to use both.”

(From the Cornell University Library.)


Richard Feynman tangled regularly with military censors at Los Alamos. Playing one day with a computing machine, he discovered a pleasing little pattern:

1/243 = 0.004115226337448559670781893004115226337448559670781893004115226…

“It’s quite cute, and then it goes a little cockeyed when you’re carrying; confusion occurs for only about three numbers, and then you can see how the 10 10 13 is really equivalent to 114 again, or 115 again, and it keeps on going, and repeats itself nicely after a couple of cycles. I thought it was kind of amusing.”

Well, I put that in the mail, and it comes back to me. It doesn’t go through, and there’s a little note: ‘Look at Paragraph 17B.’ I look at Paragraph 17B. It says, ‘Letters are to be written only in English, Russian, Spanish, Portuguese, Latin, German, and so forth. Permission to use any other language must be obtained in writing.’ And then it said, ‘No codes.’

So I wrote back to the censor a little note included in my letter which said that I feel that of course this cannot be a code, because if you actually do divide 1 by 243 you do, in fact, get all that, and therefore there’s no more information in the number .004115226337… than there is in the number 243 — which is hardly any information at all. And so forth.

“I therefore asked for permission to use Arabic numerals in my letters. So, I got that through all right.”

(From his reminiscences.)