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.)


In 1995, Alma College mathematician John F. Putz counted the measures in Mozart’s piano sonatas, comparing the length of the exposition (a) to that of the development and recapitulation (b):

Köchel and movement a b a + b
279, I 38 62 100
279, II 28 46 74
279, III 56 102 158
280, I 56 88 144
280, II 56 88 144
280, II 24 36 60
280, III 77 113 190
281, I 40 69 109
281, II 46 60 106
282, I 15 18 33
282, III 39 63 102
283, I 53 67 120
283, II 14 23 37
283, III 102 171 273
284, I 51 76 127
309, I 58 97 155
311, I 39 73 112
310, I 49 84 133
330, I 58 92 150
330, III 68 103 171
332, I 93 136 229
332, III 90 155 245
333, I 63 102 165
333, II 31 50 81
457, I 74 93 167
533, I 102 137 239
533, II 46 76 122
545, I 28 45 73
547, I 78 118 196
570, I 79 130 209

He found that the ratio of b to a + b tends to match the golden ratio. For example, the first movement of the first sonata is 100 measures long, and of this the development and recapitulation make up 62. “This is a perfect division according to the golden section in the following sense: A 100-measure movement could not be divided any closer (in natural numbers) to the golden section than 38 and 62.”

Ideally there are two ratios that we could hope would hew to the golden section: The first relates the number of measures in the development and recapitulation section to the total number of measures in each movement, and the second relates the length of the exposition to that of the recapitulation and development. The first of these gives a correlation coefficient of 0.99, the second of only 0.938.

So it’s not as impressive as it might be, but it’s still striking. “Perhaps the golden section does, indeed, represent the most pleasing proportion, and perhaps Mozart, through his consummate sense of form, gravitated to it as the perfect balance between extremes,” Putz writes. “It is a romantic thought.”

(John F. Putz, “The Golden Section and the Piano Sonatas of Mozart,” Mathematics Magazine 68:4 [October 1995], 275-282.)


A charming puzzle from Crux Mathematicorum, December 2004:

If all plinks are plonks and some plunks are plinks, which of these statements must be true?

X: All plinks are plunks.
Y: Some plonks are plunks.
Z: Some plinks are not plunks.

Click for Answer