The Wikipedia page for 1024 gives a handy technique for estimating large powers of 2 in decimal notation. For exponents up to about 100,
210a+b ≈ 2b103a.
For example, 235 = 34359738368 ≈ 32 × 109 = 32000000000.
This works because 210 ≈ 103. 3a gives a good estimate of the number of digits for exponents up to 300.
(Thanks, Stephen.)
In his 1948 book The Lost Art of Profanity, Burges Johnson quotes from an opinion by a Judge Hammond of the Supreme Judicial Court of Massachusetts:
The Watch and Ward Society of Boston years ago brought charges against a certain magazine for printing obscene matter, and my old friend the late Kendall Banning was forced to defend the publication. He felt sure that he could make a case, and during the train ride to Boston he had a sudden idea, and began jotting down such nursery rhymes as he could recall. Then he crossed out significant words and substituted asterisks. In court he asked permission to read these rhymes. They later appeared in a privately printed brochure which aroused delight or horror, according to the state of the reader’s mind. A mere sampling will serve here:
A dillar, a dollar
A ten-o’clock scholar,
What makes you *** so soon?
You used to *** at ten o’clock,
But now you *** at noon.Jack and Jill went up the hill
To *******
Jack fell down and broke his ***
And Jill came tumbling after.
Johnson says that the courtroom broke out in laughter and that Banning had made his point.
04/15/2016 UPDATE: Related (thanks, Mate):
affrontee
n. an insulted or offended person
In Gelett Burgess’ 1911 novel Find the Woman, a truck driver blocks the way of a parade organized by a society to ban profanity. He is addressed by Dr. Hopbottom, the society’s head:
See here, you slack-salted transubstantiated interdigital germarium, you rantipole sacrosciatic rock-barnacle you, if you give me any of your caprantipolene paragastrular megalopteric jacitation, I’ll make a lamellibranchiate gymnomixine parabolic lepidopteroid out of you! What diacritical right has a binominal oxypendactile advoutrous holoblastic rhizopod like you got with your trinoctial ustilaginous Westphalian holocaust blocking up the teleostean way for, anyway! If you give me any more of your lunarian, snortomaniac hyperbolic pylorectomy, I’ll skive you into a megalopteric diatomeriferous auxospore! You queasy Zoroastrian son of a helicopteric hypotrachelium, you, shut your logarithmic epicycloidal mouth! You let this monopolitan macrocosmic helciform procession go by and wait right here in the anagological street. And no more of your hedonistic primordial supervirescence, you rectangular quillet-eating, vice-presidential amoeboid, either!
The truck driver apologizes: “I see a plain, sea-faring man has no show with a doctor when it comes to exhibiting language in public. … If this here society what’s running this here procession can turn out graduates of the noble art of profanity like you are, I want to say this: Give me the pledge, and I’ll sign it.”
An arrangement of three mutually perpendicular planes, like those in the corner of a cube, have a pleasing property: They’ll reflect a ray of light back in the direction that it came from. This happy fact is exploited in a variety of technologies, from laser resonators to radar reflectors; the taillights on cars and bicycles contain arrays of tiny corner reflectors.
“A more dramatic application is to reflect laser rays from the Moon, where many such devices have been in place since the 1969 Apollo mission, which sent men to the Moon for the first time,” note mathematicians Juan A. Acebrón and Renato Spigler. “Among other things, the Earth-Moon distance can be measured by firing a laser beam from the Earth to the Moon, and measuring the travel time it takes for the beam to reflect back. This has allowed an estimate of the distance to within an accuracy of 3 cm.”
(Juan A. Acebrón and Renato Spigler, “The Magic Mirror Property of the Cube Corner,” Mathematics Magazine 78:4 [October 2005], 308-311.)
Half sleepless night again — an entirely disgusting dream, about men using flesh and bones, hands of children especially, for fuel — being out of wood and coals. I took a piece to put on someones fire, and found it the side of an animals face, with the jaw and teeth in it.
— John Ruskin, Brantwood Diary, Oct. 29, 1877
I had a dream last night. An amputated head had been stuck on to a man’s trunk, making him look like a drunken actor. The head began to talk. I was terrified and knocked over my folding screen in trying to push a Russian in front of me against the furious creature’s onslaught.
— August Strindberg, Inferno, 1897
The nightmares returned — one terrible one in February 1896 about a tramp, seen holding over a well ‘washing, but with a kind of amused tenderness, an object that I thought was a rabbit, but I presently saw that it was a small deformed hairy child, with a curious lower jaw, very shallow: over the face it had a kind of horny carapace … made of some material resembling pottery. I was disgusted at this but went on, and it grew dark: I heard behind me an odd sound, and turning round saw this horrible creature only a foot or two high, walking complacently after me, with its limbs involved in ugly and shapeless clothes, made, it seemed to me, of oakum, or some more distressing material. The horror of it exceeded all belief.’
— A.C. Benson, quoted in David Newsome, On the Edge of Paradise, 1980
This is clever — in 1893 Texas inventor Martin Everhart patented a clock-winding mechanism that’s driven by rainwater. The water fills a tank in the attic and then drops through a pipe into a pail in the clock. The pail is balanced with a counterweight, so it falls and rises continuously, accepting a new measure of water at the top and discharging it at the bottom. This motion winds the clock.
I guess the whole thing would stop eventually in a drought, but the clock can be wound by hand if necessary.
In 1863 the residents of Sandy Cove, Nova Scotia, discovered a legless man on the shore of St. Mary’s Bay. He spoke no English and could not tell them who he was or where he had come from. In this week’s episode of the Futility Closet podcast we’ll tell the story of “Jerome” and what is known or guessed of his past.
We’ll also learn about explosive rats in World War II and puzzle over a computer that works better when its users sit.
During World War II the British Special Operations Executive used poetry to communicate with its agents in enemy territory. The sender and receiver would agree in advance on a poem, and by numbering its letters they produced a simple cipher that could be used to transmit messages. Because both sides could memorize the poem, there was no codebook to lose, but the Nazis could break the code fairly easily, particularly if the poem was well known.
Realizing this, SOE codes officer Leo Marks began to introduce original poems of his own creation. He gave this one to French agent Violette Szabo in March 1944:
The life that I have is all that I have,
And the life that I have is yours.
The love that I have of the life that I have
Is yours and yours and yours.
A sleep I shall have, a rest I shall have,
Yet death will be but a pause.
For the peace of my years in the long green grass
Will be yours and yours and yours.
Marks had written it three months earlier in memory of his girlfriend Ruth, who had died in a plane crash in Canada. The poem became famous when it was read in the 1958 film Carve Her Name With Pride, about Szabo’s exploits in the war. Unfortunately, Szabo herself was captured, tortured, and killed before she could transmit any messages.
If you mark two points on a circle, A and B, and a third point T, then angle ATB remains constant as T moves along the segment between A and B. (If you mark a point S in the circle’s other segment then you get another constant angle, ASB, and ASB = 180 – ATB.)
If two circles intersect at A and B and we move T as before along the segment opposite the second circle, and we extend TA and TB to P and Q on the second circle, then the length of chord PQ remains constant as T moves.
(From David Wells, The Penguin Dictionary of Curious and Interesting Geometry, 1992.)
