A Friedman number, named after Stetson University mathematician Erich Friedman, is a number that can be calculated using its own digits, such as 736 = 36 + 7 or 3281 = (38 + 1) / 2.
A “nice” Friedman number is one in which the digits are used in order, such as 3685 = (36 + 8) × 5 or 3972 = 3 + (9 × 7)2.
Might this be done in other number systems? In a sense all Roman numerals are automatically Friedman numbers, but there are some interesting nontrivial examples as well:
XVIII = IV × II + X
LXXXIII = IXX×X/L + II
And it turns out that “nice” examples are possible here too, in which a number’s letters are used in order:
LXXVI = L / X × XV + I
LXXXIV = LX / X × XIV
Is there more? Friedman has begun looking for examples in Mayan numerals — see his website.
When Croatian artists Olinka Vištica and Dražen Grubišic ended their four-year relationship in 2003, they joked about creating a museum to house all their leftover personal items. “We were thinking of how to preserve the beautiful moments we had together and not destroy everything,” Vištica said. Three years later, Grubišic suggested that they do this in earnest, and they created the Museum of Broken Relationships, displaying items left over from breakups around the world.
After ending an 18-month relationship with an abusive lover, a Toronto woman sent in a necklace and earrings he had given her. “The necklace was given as an apology after one night of abuse. He used it as leverage that I should do as he said. I finally broke it off. I keep the necklace as a reminder of what to look out for.”
A Berlin women donated the ax she’d used to chop up her partner’s furniture after she left her for another woman. “Every day I axed one piece of her furniture. I kept the remains there, as an expression of my inner condition. The more her room filled with chopped furniture acquiring the look of my soul, the better I felt. Two weeks after she left, she came back for the furniture. It was neatly arranged into small heaps and fragments of wood. She took that trash and left my apartment for good. The axe was promoted to a therapy instrument.”
Between 2006 and 2010, the collection toured the world and was seen by 200,000 people. It’s now found a permanent home in Zagreb, and in 2016 it opened another location in Los Angeles, next to the theater that hosts the Oscars. “I think in periods of suffering people become creative, and I think this is a catharsis,” Vištica told The Star. “I think that relationships, especially love relationships, influence us so much and they make us the people we are.”
“If you bet on a horse, that’s gambling. If you bet you can make three spades, that’s entertainment. If you bet cotton will go up three points, that’s business. See the difference?” — Blackie Sherrod
In 1703, London had a strange visitor, a young man who ate raw meat and claimed that he came from an unknown country on the island of Taiwan. Though many doubted him, he was able to answer any question he was asked, and even wrote a best-selling book about his homeland. In this week’s episode of the Futility Closet podcast we’ll consider the curious question of the man from Formosa.
We’ll also scrutinize a stamp forger and puzzle over an elastic Utah.
A 1907 magazine reports two curiously ingrown family trees. The first is that of an alleged Neapolitan sailor:
I married a widow. She had by her first husband a handsome girl named Silvietta, with whom my father fell in love and who became his second wife. Thus my father became my son-in-law and my stepdaughter became my mother, since she had married my father. Soon afterward my wife gave birth to a son, who became my father’s stepbrother and at the same time my uncle, since he was my stepmother’s brother.
But that was not all, for in due time my father’s wife also gave birth to a boy, who was my brother and also my stepson [grandson?], since he was the son of my daughter. My wife was also my grandmother, for she was the mother of my mother, and thus I was my wife’s husband and at the same time her grandson. Finally, as the husband of a person’s grandmother is naturally that person’s grandfather, I am forced to the conclusion that I am my own grandfather.
We’ve seen that before, but the second story describes a more complicated route to the same outcome. Fifteen-year-old Ida Kriebel of Pennsylvania married 60-year-old Jacob Doney and became her own grandmother:
Domey’s first wife was the widow of John Wieden. She had three more children by Doney. One of her children married Samuel Kriebel, and a year later died. The widower married again. From this second union came Ida Kriebel. By this arrangement Doney became the stepgrandfather of his own child [wife?].
“The second Mrs. Doney also became stepgrandmother of twenty-five men and women, and stepgreat-grandmother of a lot of boys and girls of about her own age.”
Edric Cane came up with a simple way to establish any row in Pascal’s triangle, creating a simple sequence of fractions that, when multiplied successively, will produce the numbers in any desired row. Here’s an example for Row 7, giving the coefficients for (a + b)7 = a7 + 7a6b + 21a5b2 + 35a4b3 + 35a3b4 + 21a2b5 + 7ab6 + b7:
All of Johann Sebastian Bach’s surviving brothers were named Johann: Johann Rudolf, Johann Christoph, Johann Balthasar, Johannes Jonas, and Johann Jacob. His father was Johann Ambrosius Bach, and his sister was Johanna Juditha.
By contrast, his other sister, Marie Salome, “stuck out like a sore thumb,” writes Jeremy Siepmann in Bach: Life and Works. “And they all had grandparents and uncles and cousins whose names were also Johann, something. Johann Sebastian’s own children included Johann Gottfried, Johann Christoph, Johann August, Johann Christian, and Johanna Carolina.”
Several sources define vacansopapurosophobia as “fear of blank paper” — it’s not in the Oxford English Dictionary, but it’s certainly a useful word.
I’ve also seen artiformologicalintactitudinarianisminist, “one who studies 4-5-letter Latin prefixes and suffixes.” I don’t have a source for that; it’s not in the OED either.
In Say It My Way, Willard R. Espy defines a cypripareuniaphile as “one who takes special pleasure in sexual intercourse with prostitutes” and acyanoblepsianite as “one who cannot distinguish the color blue.”
In By the Sword, his history of swordsmen, Richard Cohen defines tsujigiri as “to try out a new sword on a chance passerby.” Apparently that’s a real practice.
And one that is in the OED: mallemaroking is “the boisterous and drunken exchange of hospitality between sailors in extreme northern waters.”
Miss Alice E. Lewis sent this curiosity to the Strand in 1903:
These false horseshoes were found in the moat at Birtsmorton Court, near Tewkesbury. It is supposed that they were used in the time of the Civil Wars, so as to deceive any person tracking the marks. The one on the left is supposed to leave the mark of a cow’s hoof, the one on the right that of a child’s foot.
The same idea has been used by moonshiners and patented at leasttwice. Does this really work?
“If God wants us to do a thing, He should make his wishes sufficiently clear. Sensible people will wait till He has done this before paying much attention to Him.” — Samuel Butler (from his notebook)
