Doing Some Twenty on Ninety
Recently I read Bunny Crumpacker's* Perfect Figures : The Lore of Numbers and How we Learned to Count (New York : St. Martin's Press, 2007, 271 pages). I never quite decided whether I liked it or not, but I rather enjoyed the reading of it. Mostly it was engaging, but the style took me a while to loosen up and enjoy. For more you are welcome to my book note.
Regardless of the overall effect, there were plenty of amusing bits and I have, naturally, kept a few to share with you.
This first item we should probably file under "the more things change, the more they stay the same". The time was apparently late July 1918 (per this page of waltz history).
The waltz grew out of the ländler, a German country dance in three-quarter. time. The word waltz is from an old German word, walzen, which meant "to roll," "turn," or "glide." The ländler involved a certain amount of countryish hopping and jumping, but the waltz polished all that with a gliding grace that had enormous appeal for the young men and women who first danced it.
It also meant that the man held the woman in a light embrace as they danced–scandal! The aristocratic dances that preceded it–the minuets, polonaises, and quadrilles–kept the partners at a decorous distance from each other. but waltzers had to hold on to each other as they swooped around the dance floor. The waltz was banned in parts of southern Germany and Switzerland. Religious leaders everywhere considered it to be vulgar and sinful.
When the waltz reached England, the Times of London considered it necessary to write an editorial about its lasciviousness. "It is quite sufficient to cast ones eyes on the voluptuous intertwining of the limbs and close compressure on the bodies in their dance, to see that it is indeed far removed from the modest reserve which has hitherto been considered distinctive of English females. So long as this obscene display was confined to prostitutes and adulteresses, we did not think it deserving of notice; but now that it is attempted to be forced on the respectable classes of society by the civil examples of their superiors, we feel it a duty to warn every parent against exposing his daughter to so fatal a contagion." On to the tango! [pp. 70–71]
Despite all that it seems that Queen Victoria was a devotee of the waltz.
Next, for our delectation, a bit of unexpected rudeness from St. Jerome (I figure him for the most sour saint in the bunch, if not the biggest sourpuss in history) and a fun euphemism that some hip-hopsters might like to consider. The topic at hand is ways to count to high numbers on the hands.
Finger numbers eventually began to have meanings beyond pure numeration. Saint Jerome wrote that the finger-counting sign for thirty meant marriage. The tip of the index finger was held against the tip of the thumb–thus, he wrote, "a tender kiss represents the husband and the wife." Sixty, with the index finger bent over the thumb on the left hand, so that its second joint touched the thumb's tip, represented a widow "in sadness and tribulation." One hundred ("pay close attention, gentle reader," he wrote), used the same fingers on the right hand, with the tip of the index finger touching the bottom section of the thumb and the space between them closed, "shows the crown of virginity."
Less tenderly, in ancient Persia a poet wrote of the battle between two noblemen. "They fight day and night to decide which army shall do a twenty on the other's ninety." The hand sign for twenty placed the thumb of the right hand between the index and third fingers, so that it protruded (a relative of today's erect middle finger). The ninety, on the right hand, involved curling the index finger so that its tip touched the bottom of the thumb, leaving a small round hole (not the closed virgin's crown, but now open, perhaps an anus) between the two fingers. Doing the twenty on the ninety wasn't a nice thing to say, even for a poet. [p. 79]
Next, from the chapter on "11", some mocking of conspiracy theorists and god-fearing wackos, who might be the same people.
The World Trade Towers were eleven incarnate, and an amazing eleven aura has risen up around them since the terrible day on which they fell. The cult of eleven begins with the attack that took place on September 11. In numbers, the date is known as 9/11, and nine plus one plus one is eleven. The first plane to hit the North Tower was American Airlines Flight 11. It had ninety-two passengers; nine plus two is eleven. Flight 77 hit the Pentagon; seventy-seven is eleven times seven; it held sixty-five passengers; five plus six is eleven. September 11 is the 254th day of the year; two plus five plus four is eleven. After September 11, 111 days remain until the end of the year. The emergency code for telephones is 911–nine-one-one, which is eleven, or nine-eleven. The state of New York was the eleventh state to join the Union; New York City is spelled with eleven letters. Afghanistan, where bin Laden was thought to be hiding, has eleven letters. The Twin Towers looked like an eleven. And each tower had 110 floors, which is eleven times ten.
Is this an amazing series of coincidences? Or, as some believe, is it a message from God? But surely, if God wanted to send us a message–about our wicked ways, or the coming of the Messiah, or the Second Coming and the imminent end of the world–he wouldn't send it in code. He spoke clearly–albeit through an angel–to Mary, among others; he spoke directly to Moses, and left his words chiseled in stone. Why would he bother with coeds? Nearly three thousand people died on 9/11; many more suffered their loss and were left to grieve. It's hard to imagine a god counting the letters in New York City and deciding that those thousands of people, and all who loved them, should suffer as they did so that eleven could stand as a warning. Skywriting would have been a lot better. [pp. 192–193]
Since this is a book about numbers, here are a few fun facts from number theory that might earn one a free beer some night at the bar.
The Fibonacci numbers have a happy–and odd–eleven quirk. Any ten Fibonacci numbers in a sequence will always add up to a number that's divisible by eleven. The first ten numbers: 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 143, and 143 divided by 11 is 13. Or, to use higher numbers, continuing the sequence: 55 + 89 + 144 + 233 + 377 + 610 + 987 + 1,597 + 2,584 + 4,181 = 10,857, and 10,857 divided by 11 is 987. There's more: the sum of any sequence of ten Fibonacci numbers when divided by eleven always gives a number that is the seventh number in the sequence. In the first example above, 13 is the seventh number in the sequence; in the second, 987 is. Is this more Fibonacci magic? Absolutely. [pp. 196–197]
Finally, a whirlwind explanation of the archaic English monetary system, for those of us who still read older English novels and never quite caught on to all the names for the money, names that seem to proliferate like nicknames for characters in Russian novels.
The English pound in the duodecimal system (adjective, relating to the number twelve, from the Latin duodecimus, "twelfth," from duodecim, "twelve," from duo, "two," and decem, "ten") was divided into 240 pence. The singular of pence is penny, and the symbol for penny is p, so for the five pence, the Brits write "5 p," which they pronounce "five pee".
Each twelve pence was equal to one shilling, and twenty shillings made a pound. Which doesn't say anything about farthings, bobs, florins, crowns, or guineas. There were four farthings to a penny (or two halfpennies). Farthings, halfpennies, and pennies were all kn9own as coppers–because, yes, there were all made of copper. A florin was worth two shillings. A shilling was the same as a bob (and bob wasn't used in the plural–fifteen shillings was fifteen bob); a five-shilling piece was a crown; a guinea was worth just over a pound. A sovereign was a gold pound coin. Quid is the slang term for pound; the plural of pound is pounds, but the plural of quid is still quid. [pp 202–203]
———-
* I don't plan to make fun of Bunny's name, but I do have two of her earlier books–both cookbooks, by the way, of nostalgic, vintage recipes–and I have always thought her name delightfully outlandish.
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on Saturday, 6 December 2008 at 23.13
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The English pound in the duodecimal system […] was divided into 240 pence. The singular of pence is penny, and the symbol for penny is p, so for the five pence, the Brits write "5 p," which they pronounce "five pee".
this is wrong. Dealing with the pre-1991, pre-decimal pound, where there are 240 pence in the pound [and 100 pence is eight-and-fourpence], the symbol for a penny was d (from Latin, denarius). If you had 5d in your pocket, you'd pronounce it "fivepence" (*)
If you had 5p in your pocket, you're dealing with the decimal, post 1971 pound, in which there are only 100 pence to the pound. 5p is indeed pronounced "five pee" (though if you say "fivepence" people will know what you mean); that sum of money, being 1/20 of a pound, is the equivalent of an old shilling. The old shilling coins circulated, renamed/ redenominated "5p" for nearly 20 years, until new, smaller 5p coins were issued.
He doesn't (in this excerpt) mention that the abbreviation for shilling is s, not short for "shilling" but for "solidus", another Roman coin. If you wanted to talk about ten shillings and sixpence [half a guinea, by the way], you would write it as "10s 6d" or more quickly "10/6", pronounced "ten and six". I refer the reader to the Mad Hatter, whose chapeau was that price (in this style, 10/6), at least in the Tenniel illustration.
(*)5d was probably made up of a 3d coin (threepenny bit, pronounced "thruppence") and tuppence in coppers – farthings, halfpennys (ha'penny, pronounced "hay-penny", exactly an inch across) and pennies. I grew up with this stuff, and it becomes second nature, but decimal is MUCH easier.
oh, and "quid" and "bob" are not nouns with no plural (biiig arnold zwicky pointed this out to me), they are words like "sheep" and "salmon", where the singular form is identical to the plural form.
on Sunday, 21 December 2008 at 00.28
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Now that things are settling down a bit, I can finally say "Thanks, Chris!" for sorting that out. it probably won't surprise you at all to learn that Rod Williams took care of the same when the note appeared at my facebook page. Phew. By the way, I know exactly which illustration of the Mad Hatter you mean, and I'm happy to have that detail correct now.
on Sunday, 21 December 2008 at 14.25
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so whats with the facebook duplication?
should i abandon the blog and just read you in facebook-land?
– – curious in toronto
on Wednesday, 24 December 2008 at 10.10
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Not at all; this is the ur-blog and it's much more fun to have you here. Facebook imports the "notes" for me for the benefit [!] of a few friends who don't stop by here regularly and Rod seized his opportunity.