In 1629, a Dutch trading vessel struck a reef off the coast of Australia, marooning 180 people on a tiny island. As they struggled to stay alive, their leader descended into barbarity, gathering a band of cutthroats and killing scores of terrified castaways. In this week’s episode of the Futility Closet podcast we’ll document the brutal history of Batavia’s graveyard, the site of Australia’s most infamous shipwreck.
We’ll also lose money in India and puzzle over some invisible Frenchmen.
In Circularity, Ron Aharoni mentions a story by Raymond Smullyan. On a certain island there are two kinds of people, those who always lie and those who always tell the truth. One day an islander is arrested on suspicion of murder. At his trial he says, “The murderer is a liar.”
Smullyan argues that this piece of evidence alone should acquit him. If the man is honest, then what he says is true, the murderer is a liar, and since he himself is a truth-teller he cannot be the guilty party. On the other hand, if he’s a liar then his testimony is false, which means that the murderer is in fact not a liar, and once again he cannot be guilty. Either way, he proves his innocence by showing that the murderer and himself belong to two different tribes.
Aharoni adds, “The problem is that the man was found beside the corpse with a bloody knife in his hand and a wide smile on his face. He is obviously the murderer, which means that he managed to prove an obvious fallacy. It seems that using his method, he can prove anything. And indeed he can. See what he is claiming when stating that the murderer is a liar: ‘If I am the murderer, then I am a liar’, which means ‘if I am the murderer then this is a lie’. In other words — ‘If I am the murderer then L is true’. And … this proves that ‘I am not the murderer.'”
When J.R.R. Tolkien wrote his first story, at age 7, “my mother … pointed out that one could not say ‘a green great dragon,’ but had to say ‘a great green dragon.’ I wondered why, and still do.” It turns out that there’s an unwritten rule in English that governs the order in which we string our adjectives together:
opinion
size
age
shape
color
origin
material
type
purpose
In The Elements of Eloquence, Mark Forsyth writes, “So you can have a lovely little old rectangular green French silver whittling knife. But if you mess with that word order in the slightest you’ll sound like a maniac. It’s an odd thing that every English speaker uses that list, but almost none of us could write it out.”
Another unwritten rule concerns ablaut reduplication: In terms such as chit-chat or dilly-dally, in which a word is repeated with an altered vowel, the vowels will follow the pattern I-A-O if there are three words and I-A or I-O if there are two. So:
tip-top
clip-clop
King Kong
flip-flop
sing-song
shilly-shally
And so on. Interestingly, these rules about precedence seem to follow a precedence rule of their own: The “royal order of adjectives” would require Red Riding Hood to meet the “Bad Big Wolf” (opinion before size). But the rule of ablaut reduplication apparently trumps this, making him the Big Bad Wolf.
“Why this should be is a subject of endless debate among linguists,” Forsyth writes. “It might be to do with the movement of your tongue or an ancient language of the Caucasus. It doesn’t matter. It’s the law, and, as with the adjectives, you knew it even if you didn’t know you knew it. And the law is so important that you just can’t have a Bad Big Wolf.”
I don’t know how this applies to dragons.
(Thanks, Nick and Armin.)
Michael Grab balances rocks. He regards it as a combination of art, engineering, and contemplative spiritual practice combining patience, critical thinking, and problem solving. But the only “ingredients” in his sculptures are rocks and gravity — there’s no mortar, cement, or artificial support holding them together; any one of them can be toppled with a finger.
“The most fundamental element of balancing in a physical sense is finding some kind of ‘tripod’ for the rock to stand on. Every rock is covered in a variety of tiny to large indentations that can act as a tripod for the rock to stand upright, or in most orientations you can think of with other rocks. By paying close attention to the feeling of the rocks, you will start to feel even the smallest clicks as the notches of the rocks in contact are moving over one another.”
“There is nothing easy about it. It can frustrate me to my limits, and then I learn. Or it can reveal magic beyond words, and I learn. Sometimes the rock wins, but most of the time I win.”
From the St. Louis Post-Dispatch, via the Ohio Law Reporter, Aug. 17, 1908: During a dispute over a will in Vienna, a phonograph record was introduced into evidence so that the dead woman herself could explain her intentions, which she’d recorded during her lifetime:
Prof. Sulzer stated that he had a phonographic record that would settle beyond question the point in dispute and asked the court’s permission to introduce it as evidence. The permission was granted and Mme. Blaci, the decedent, told in her own voice of her affection for her brother and his family and announced her intention of providing before her death so that her nephew, Heinrich, would be well cared for after she had passed away.
Heinrich testified that the record was made on the twenty-first anniversary of his birth. Mme. Blaci, he told the judge, had said at the time that she wanted the words she had spoken to her brother, Heinrich’s father, put on record as a souvenir of her affection that could be handed down to her nephew.
“After hearing the record, the court immediately awarded Heinrich $120,000 as his share of the estate, which was the full amount claimed by him.”
In 1986 British electronics engineer Lee Sallows invented the alphamagic square:
As in an ordinary magic square, each row, column, and long diagonal produces the same sum. But when the number in each cell is replaced by the length of its English name (25 -> TWENTY-FIVE -> 10), a second magic square is produced:
Now British computer scientist Chris Patuzzo, who found the percentage-reckoned pangram that we covered here in November 2015, has created a double alphamagic square:
Each row, column, and long diagonal here totals 303370120164. If the number in each cell is replaced by the letter count of its English name (using “and” after “hundred,” e.g. ONE HUNDRED AND FORTY-EIGHT BILLION SEVEN HUNDRED AND TWENTY-EIGHT MILLION THREE HUNDRED AND SEVENTY-EIGHT THOUSAND THREE HUNDRED AND SEVENTY-EIGHT), then we get a new magic square, with a common sum of 345:
And this is itself an alphamagic square! Replace each number with the length of its name and you get a third magic square, this one with a sum of 60:
Chris has found 50 distinct doubly alphamagic squares, listed here. I suppose there must be some limit to this — is a triple alphamagic square even possible?
(Thanks, Chris and Lee.)
There was an old man who said, “Do
Tell me how I’m to add two and two!
I’m not very sure
That it does not make four,
But I fear that is almost too few.”
A mathematician confided
A Möbius strip is one-sided.
You’ll get quite a laugh
If you cut one in half,
For it stays in one piece when divided.
A mathematician named Ben
Could only count modulo ten.
He said, “When I go
Past my last little toe,
I have to start over again.”
By Harvey L. Carter:
‘Tis a favorite project of mine
A new value of π to assign.
I would fix it at 3,
For it’s simpler, you see,
Than 3.14159.
J.A. Lindon points out that 1264853971.2758463 is a limerick:
One thousand two hundred and sixty
four million eight hundred and fifty
three thousand nine hun-
dred and seventy one
point two seven five eight four six three.
From Dave Morice, in the November 2004 Word Ways:
A one and a one and a one
And a one and a one and a one
And a one and a one
And a one and a one
Equal ten. That’s how adding is done.
(From Through the Looking-Glass:)
‘And you do Addition?’ the White Queen asked. ‘What’s one and one and one and one and one and one and one and one and one and one?’
‘I don’t know,’ said Alice. ‘I lost count.’
‘She can’t do Addition,’ the Red Queen interrupted.
An anonymous classic:
The integral z-squared dz
From one to the cube root of three
Times the cosine
Of three pi over nine
Equals log of the cube root of e.
A classic by Leigh Mercer:
A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.
UPDATE: Reader Jochen Voss found this on a blackboard at Warwick University:
If M’s a complete metric space
(and non-empty), it’s always the case:
If f’s a contraction
Then, under its action,
Exactly one point stays in place.
And Trevor Hawkes sent this:
A mathematician called Klein
Thought the Möbius strip was divine.
He said if you glue
The edges of two
You get a nice bottle like mine.
In 1987, Portuguese poet Alberto Pimenta took the sonnet Transforma-se o amador na cousa amada (The lover becomes the thing he loves), by the 16th-century poet Luís de Camões, and rearranged the letters of each line to produce a new sonnet, Ousa a forma cantor! Mas se da namorada (Dare the form, songster! But if the girlfriend).
Here’s Camões’ (curiously apposite) original poem, translated by Richard Zenith:
The lover becomes the thing he loves
by virtue of much imagining;
since what I long for is already in me,
the act of longing should be enough.
If my soul becomes the beloved,
what more can my body long for?
Only in itself will it find peace,
since my body and soul are linked.
But this pure, fair demigoddess,
who with my soul is in accord
like an accident with its subject,
exists in my mind as a mere idea;
the pure and living love I’m made of
seeks, like simple matter, form.
Carlota Simões and Nuno Coelho of the University of Coimbra calculated that the letters in Camões’ sonnet can be rearranged within their lines in 5.3 × 10312 possible ways.
Interestingly, after Pimenta’s anagramming there were two letters left over, L and C, which are the initials of the original poet, Luís de Camões. “It seems that, in some mysterious and magical way, Luís de Camões came to reclaim the authorship of the second poem as well.”
In 2014, when designer Nuno Coelho challenged his multimedia students to render the transformation, Joana Rodrigues offered this:
Related: In 2005 mathematician Mike Keith devised a scheme to generate 268,435,456 Shakespearean sonnets, each a line-by-line anagram of the others. And see Choice and Fiction.
(Carlota Simões and Nuno Coelho, “Camões, Pimenta and the Improbable Sonnet,” Recreational Mathematics Magazine 1:2 [September 2014], 11-19.)
Noted in passing: In the May 2004 issue of Word Ways, Max Maven notes that “English words containing ‘ag’ almost invariably have negative meanings, usually rather harsh.” He cites BRAG, DRAG, FLAG, GAG, HAG, LAG, NAG, RAG, SAG, SLAG, SNAG, and SWAG, among others.
In May 1984 Bruce Price pointed out that words rhyming with ash tend to be “words of terrible action, of great vigor and violence”:
BASH, BRASH, CLASH, CRASH, DASH, FLASH, GASH, GNASH, HASH, LASH, MASH, PASH, PLASH, RASH, SLASH, SMASH, SPLASH, STASH, THRASH, TRASH
There are exceptions, of course. I wonder if there are any similar patterns among positive words?
In his Book of Good Love (1330), Juan Ruiz tells of a silent debate between Greece and Rome. The Romans had no laws and asked the Greeks to give them some. The Greeks feared that they were too ignorant and challenged them first to prove themselves before the wise men of Greece. The Romans agreed to a debate but asked that it be conducted in gestures, as they did not understand the Greek language. The Greeks put forward a learned scholar, and the Romans, feeling themselves at a disadvantage, put forward a ruffian and told him to use whatever gestures he felt inspired to make.
The two mounted high seats before the assembled crowd. The Greek held out his index finger, and the Roman responded with his thumb, index, and middle fingers. The Greek held out his open palm, and the Roman responded with a fist. Then the Greek announced that the Romans deserved to be given laws.
Each side then asked its champion to explain what had happened.
They asked the Greek what he had said to the Roman by his gestures, and what he had answered him. He said: ‘I said that there is one God; the Roman said He was One in Three Persons, and made a sign to that effect.
Next I said that all was by the will of God; he answered that God held everything in his power, and he spoke truly. When I saw that they understood and believed in the Trinity, I understood that they deserved assurance of [receiving] laws.’
They asked the hoodlum what his notion was; he replied: ‘He said that with his finger he would smash my eye; I was mighty unhappy about this and I got mighty angry, and I answered him with rage, with answer, and with fury,
that, right in front of everybody, I would smash his eyes with my two fingers and his teeth with my thumb; right after that he told me to watch him because he would give me a big slap on my ears [that would leave them] ringing.
I answered him that I would give him such a punch that in all his life he would never get even for it. As soon as he saw that he had the quarrel in bad shape, he quit making threats in a spot where they thought nothing of him.’
Ruiz writes, “This is why the proverb of the shrewd old woman says, ‘No word is bad if you don’t take it badly.’ You will see that my word is well said if it is well understood.”
(From Laura Kendrick’s The Game of Love, 1988.)
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