On each of these two black lines is a trio of red points marked by the same distances.
The midpoints of segments drawn between corresponding points are collinear.
(Discovered by Danish mathematician Johannes Hjelmslev.)
Unquote
“I never know whether to pity or congratulate a man on coming to his senses.” — Thackeray
Headlong
There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that ‘remembered’ a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.
— Bertrand Russell, The Analysis of Mind, 1921
Misc
- Liza Minnelli, daughter of Judy Garland, married Jack Haley Jr., son of the Tin Man.
- The Netherlands still sends 20,000 tulip bulbs to Canada each year.
- Every positive integer is a sum of distinct terms in the Fibonacci sequence.
- HIDEOUS and HIDEOUT have no vowel sounds in common.
- “Death is only a larger kind of going abroad.” — Samuel Butler
(Thanks, Colin and Joseph.)
Melodic Puns
In Leonard Bernstein’s Mass, in which the phrase “me and my soul” is sung repeatedly, the words me and soul are sung to the notes mi and sol.
In the song “Sodomy” in the 1967 rock musical Hair, the word sodomy is sung to the notes so, do, and mi.
(From Dave Morice, The Dictionary of Wordplay, 2001.)
06/13/2024 UPDATE: In 1955, entomologists James Brennan and D. Elden Beck named two new species of chigger Trombicula doremi and Trombicula fasola.
Day Tripper
A letter from Lewis Carroll to Nature, March 31, 1887:
Having hit upon the following method of mentally computing the day of the week for any given date, I send it you in the hope that it may interest some of your readers. I am not a rapid computer myself, and as I find my average time for doing any such question is about 20 seconds, I have little doubt that a rapid computer would not need 15.
Take the given date in 4 portions, viz. the number of centuries, the number of years over, the month, the day of the month.
Compute the following 4 items, adding each, when found, to the total of the previous items. When an item or total exceeds 7, divide by 7, and keep the remainder only.
The Century-Item. — For Old Style (which ended September 2, 1752) subtract from 18. For New Style (which began September 14) divide by 4, take overplus from 3, multiply remainder by 2. [The Century-Item is the first two digits of the year, so for 1811 take 18.]
The Year-Item. — Add together the number of dozens, the overplus, and the number of 4’s in the overplus.
The Month-Item. — If it begins or ends with a vowel, subtract the number, denoting its place in the year, from 10. This, plus its number of days, gives the item for the following month. The item for January is ‘0’; for February or March (the 3rd month), ‘3’; for December (the 12th month), ’12.’ [So, for clarity, the required final numbers after division by 7 are January, 0; February, 3; March, 3; April, 6; May, 1; June, 4; July, 6; August 2; September, 5; October, 0; November, 3; and December, 5.]
The Day-Item is the day of the month.
The total, thus reached, must be corrected, by deducting ‘1’ (first adding 7, if the total be ‘0’), if the date be January or February in a Leap Year: remembering that every year, divisible by 4, is a Leap Year, excepting only the century-years, in New Style, when the number of centuries is not so divisible (e.g. 1800).
The final result gives the day of the week, ‘0’ meaning Sunday, ‘1’ Monday, and so on.
Examples
1783, September 18
17, divided by 4, leaves ‘1’ over; 1 from 3 gives ‘2’; twice 2 is ‘4.’
83 is 6 dozen and 11, giving 17; plus 2 gives 19, i.e. (dividing by 7) ‘5.’ Total 9, i.e. ‘2.’
The item for August is ‘8 from 10,’ i.e. ‘2’; so, for September, it is ‘2 plus 3,’ i.e. ‘5.’ Total 7, i.e. ‘0,’ which goes out.
18 gives ‘4.’ Answer, ‘Thursday.’
1676, February 23
16 from 18 gives ‘2.’
76 is 6 dozen and 4, giving 10; plus 1 gives 11, i.e. ‘4.’ Total ‘6.’
The item for February is ‘3.’ Total 9, i.e. ‘2.’
23 gives ‘2.’ Total ‘4.’
Correction for Leap Year gives ‘3.’ Answer, ‘Wednesday.’
(Via Edward Wakeling, Rediscovered Lewis Carroll Puzzles, 1995.)
Pith
“One thing you must always remember about Roosevelt is that he is about seven years old.” — Cecil Spring-Rice
Simple Enough
“It often happens that the easiest dissection puzzles are the prettiest,” wrote Henry Dudeney in 1914. “Here is a new one that ought to give the reader very little trouble. Cut the figure into five pieces that will fit together and form a square.”
Oh
This is a floodlight photographed at night. What are the segmented stalks that seem to surround it? The phenomenon is seen regularly in photographs and videos; cryptozoologists and students of UFOs call the entities rods.
In 2003 author Robert Todd Carroll consulted entomologist Doug Yanega, who explained that they’re flying insects (in this case moths).
“Essentially what you see is several wingbeat cycles of the insect on each frame of the video, creating the illusion of a ‘rod’ with bulges along its length,” Yanega wrote. “The blurred body of the insect as it moves forward forms the ‘rod,’ and the oscillation of the wings up and down form the bulges.”
“Some hilarious photographs of ‘rods’ have been posted on the Internet,” Carroll noted. “My favorite is ‘the swallow chases a rod’ which looks just like a bird going after an insect.”
Concise
Two hundred kilometers west of Pretoria is a farm called Tweebuffelsmeteenskootmorsdoodgeskietfontein. The name, the longest place name in South Africa, means “the spring where two buffaloes were shot stone dead with one shot.”
As a daughter language of Dutch, Afrikaans is capable of almost endless compounding, at least in principle. In his 1982 Total Book of South African Records, Eric Rosenthal claims that the longest word in the language is Tweedehandsemotorverkoopsmannevakbondstakingsvergaderingsameroeperstoespraakskrywerspersverklaringuitreikingsmediakonferensieaankondiging, “issuable media conference’s announcement at a press release regarding the convener’s speech at a secondhand car dealership union’s strike meeting.” But, as with many such records, the word was contrived expressly and is not in common use.