• Discussion of Salisbury Cathedral from the Bishop’s Grounds (1823) at Wikipedia
• Discussion of Salisbury Cathedral from the Bishop’s Grounds (1823) at Wikipedia
You have two glasses each filled with exactly the same amount of liquid. One contains water, the other contains wine. First, take a teaspoon of water from the water glass and pour it into the wine glass. Next stir the wine and water until well mixed. Then take a teaspoon of the water-and-wine mixture and pour it into the glass of water.
The question now is: Is there more wine in the water glass than water in the wine glass, or is there less? (from World’s Most Baffling Puzzles, Charles Barry Townsend, Sterling, New York, 1991)
(Scroll down for answer)
Oenometry means “wine-measurement”, from ancient Greek οἶνος, oinos, “wine”, + μετρία, metria, “measurement”. Its standard pronunciation would be “ee-NOM-ett-ry”, but you could conceivably say “oh-een-NOM-ett-ry” or “oi-NOM-ett-ry”.
Discussion of the answer
The original question is fair but worded to send you astray. By using the words “glass” and “teaspoon”, it creates distinct images in your mind: those of an unvarying teaspoon and of two glasses with identical-but-varying amounts of wine and water in them. So you’re guided away from considering that the contents of the glasses can be measured in teaspoons too. If you think not in teaspoons but in unspecified units (of liquid measure), it’s easier to see the truth.
If the two glasses each contain n units of liquid, by transferring water to the wine you’re adding 1 unit of water to n units of wine.
Therefore the wine glass contains n+1 units of mixed wine-and-water, of which n units are wine and 1 unit is water. Let’s say n+1 = n1.
Consider that 1 unit of that mixture contains n/n1 parts of wine and 1/n1 parts of water: n/n1 + 1/n1 = (n+1)/n1 = n1/n1 = 1 unit.
Now, if one unit of the mixture is transferred to the water glass, you take n/n1 units of wine from n units of wine in the wine glass: n – n/n1 = n-1 + 1/n1. You also take 1/n1 units of water from 1 unit of water in the wine glass: 1 – 1/n1 = (n1-1)/n1 = n/n1. So the wine glass now contains n-1 + 1/n1 units of wine and n/n1 of a unit of water.
When you add that unit to the (n-1) units of water in the water glass, it will contain (n-1) + 1/n1 units of water and n/n1 of unit of wine:
Wine glass: n-1 + 1/n1 units of wine and n/n1 of a unit of water
Water glass: n-1 + 1/n1 units of water and n/n1 of a unit of wine
Therefore, however much water and wine you start with, in the end there will be as much water in the wine glass as there is wine in the water glass. For some concrete examples:
Water glass: 2 teaspoons of water
Wine glass: 2 teaspoons of wine
2. Transfer water to wine glass and mix:
Water glass: 2 tsp of water – 1 tsp = 1 tsp of water
Wine glass: 2 tsp of wine + 1 tsp of water = 3 tsp of which 2/3 is wine, 1/3 is water
3. Transfer wine-and-water mixture to water glass:
One tsp of wine-and-water mixture = 2/3 tsp of wine + 1/3 tsp of water
Wine glass: 2 tsp of wine – 2/3 tsp of wine = 1 and 1/3 tsp of wine; 1 tsp of water – 1/3 tsp of water = 2/3 tsp of water
Water glass: 1 tsp of water + 1/3 tsp of water = 1 and 1/3 tsp of water; 0 tsp of wine + 2/3 tsp of wine = 2/3 tsp of wine
Wine glass contains: 1 and 1/3 tsp of wine, 2/3 tsp of water
Water glass contains: 1 and 1/3 tsp of water, 2/3 tsp of wine
Water glass: 10 teaspoons of water
Wine glass: 10 teaspoons of wine
Transfer water to wine glass and mix:
Water glass: 10 tsp of water – 1 tsp = 9 tsp of water
Wine glass: 10 tsp of wine + 1 tsp of water = 11 tsp of liquid of which 10/11 is wine, 1/11 is water
Transfer wine-and-water mixture to water glass:
One tsp of wine-and-water mixture = 10/11 tsp of wine + 1/11 tsp of water
Wine glass: 10 tsp of wine – 10/11 tsp of wine = 9 and 1/11 tsp of wine; 1 tsp of water – 1/11 tsp of water = 10/11 tsp of water
Water glass: 9 tsp of water + 1/11 tsp of water = 9 and 1/11 tsp of water; 0 tsp of wine + 10/11 tsp of wine = 10/11 tsp of wine
Wine glass contains: 9 and 1/11 tsp of wine, 10/11 tsp of water
Water glass contains: 9 and 1/11 tsp of water, 10/11 tsp of wine
• …ποντίων τε κυμάτων ἀνήριθμον γέλασμα… — Αἰσχύλος, Προμηθεὺς δεσμώτης (c. 479-24 B.C.)
• …of ocean-waves the multitudinous laughter… Prometheus Bound by Aeschylus* at Perseus
• …ever-glittering laughter of the far-thrown waves… (my translation)
γέλασμα, a laugh, κυμάτων ἀνήριθμον γέλασμα, Keble’s “the many-twinkling smile of Ocean, ” Aesch. — Liddell and Scott
Keble was not a sacred but, in the best sense of the word, a secular poet. It is not David only, but the Sibyl, whose accents we catch in his inspirations. The “sword in myrtle drest” of Harmodius and Aristogeiton, “the many-twinkling smile of ocean” from Æschylus, are images as familiar to him as “Bethlehem’s glade” or “Carmel’s haunted strand.” Not George Herbert, or Cowper, but Wordsworth, Scott, and perhaps more than all, Southey, are the English poets that kindled his flame, and coloured his diction. — John Keble at Penny’s Poetry Pages
One day Mr Gordon had accidentally come in, and found no one there but Upton and Eric; they were standing very harmlessly by the window, with Upton’s arm resting kindly on Eric’s shoulder, as they watched with admiration the network of rippled sunbeams that flashed over the sea. Upton had just been telling Eric the splendid phrase, “anerhithmon gelasma pontou”, which he had stumbled upon in an Aeschylus lesson that morning, and they were trying which would hit on the best rendering of it. Eric stuck up for the literal sublimity of “the innumerable laughter of the sea,” while Upton was trying to win him over to “the many-twinkling smile of ocean.” They were enjoying the discussion, and each stoutly maintaining his own rendering, when Mr Gordon entered. — quote from Frederic W. Farrar’s Eric, or Little by Little (1858) at Sententiae Antiquae
*Or possibly his son Euphorion.
(Translated and edited by Simon Whitechapel)
In the black mirroring surface of the canal, these things: a sky very high and clear, the blue infinite interior of the skull of a god2 brooding beauty and pain into the world; the walls that line the canal, white marble, sharp-edged; the vivid mosaics of precious stone with which the walls are set: oval belladonnic eyes of emerald and obsidian in faces of sculpted mammoth ivory; the mouths of jade3-lipped bayadères leaking ruby threads of wine; the topaz fingers and wrists of rhodolite4-crowned lutanists; quartz-glistered sinews in the arms of capon5-plump eunuchs fanning the dances of turquoise6-skinned odalisques who prance and beck in frozen heated showers of opal-drop sweat.
But all, in the mirroring water, is grey.7
In the black mirroring surface of the canal, these things: a broad slab of basalt to which is bound a naked man8, white against the stone’s darkness, black-haired and bound with soft unbreakable bonds of purple silk; on his belly have been painted the red strokes and hooks and curls of the ideogram for death, like the roaring fist-talon and shank of a stooping hawk9 or the opening hungry maw of a leopard10, a splash of red tissues ringed and spiked and shaped by white barbs of teeth.
But all, in the mirroring water, is grey.
In the black mirroring surface of the canal, these things: five swans; their bright, forward-sweeping eyes are set in white, oval-skulled heads that are enwedged with yellow, black-rooted beaks; their white, smooth-feathered, twice-curved necks, slender as stems, are shivered on the ripples of the passage of bodies that are white seed-pods curling to smooth, hooked tails. Five swans, silent white swans. Their beaks are small and regular as the hardened gold heads of the ritual axes of the Temple of the Thanatocrator11, which sound tchlunk tchlunk tchlunk in the skulls of the sacrifices, opening slotted, red-welling ways for the prosempyreal passage of the soul.
But all, in the mirroring water, is grey.
In the black, mirroring surface of the canal, this: the white swans clustered on the white body of the sacrifice. Their necks dart and sway, sowing moist red blooms into the fertile milk of his skin. He strains against his bonds, but the necks fall, the heads hammer with steady, unconscious grace, opening the blooms to full flower. In the mirroring water they are beautiful, like strewn blossoms12 for the feet of the Thanatocrator, who dances his hatred into the waking dreams of the world. The sacrifice is dead and the swans are streaked and smirched and spotted with gore, like heavy white flowers in a garden of torture.
Their necks bend and sway, and their beaks open and close, but in the mirroring water their voices are silent, and how may we tell what they say?
1. Trained swans were the favored form of execution under the insane and semi-legendary nymphomane Queen Sphalaghd (1-143 Anno Dominæ; 1137-1279 Anno Secundi Imperii), whose extravagances came nigh to ruining the kingdom before, after many hesitations on and retreats from the threshold, she converted fully to the austere and life-denying doctrines of the Thorn-God in the final lustrum of her nigromantically prolonged life.13 She was canonized by the Temple thirteen years after her death.
2. An obvious reference to the Thorn-God, and in another context the Yihhian (mhló)Kiùlthi might be translated “(of) the god”, but the use of the non-hieratic noun marker gives the flavor of the indefinite article in English and contributes to the sense of brooding anonymity in the story.
3. This is believed to be a satirical reference to Yokh-Tsiolphë’s own religion (see note 8 below), that of the Moon-Deity, whose abstemious priestesses wore strongly colored make-up while performing their ritual dances under the full moon.
4. From its use in other texts retrieved oneirically from the Temple, the hieroglyph appears to refer to some rose-colored semi-precious mineral, and I have chosen to translate the word as “rhodolite”: coronemus nos rosis antequam marcescant (“let us crown us with roses before they be withered”, Sapientia Solomonis 2:8) was a sentiment accepted in its widest possible sense at the week-long feasts held during the long years of Queen Sphalagdh’s dissipation.
5. Possibly a castrated form not of the domestic hen (Gallus domesticus) but of the peacock (Pavo cristatus).
6. Again a possible satirical reference to the priestesses of the Moon-Deity.
7. Mirrors in the Temple were only of dark minerals, principally basalt, haematite, and black coral (Gorgonia spp), for the priests taught that color was one of the snares of sensuality by which the world entrapped men’s souls. Accordingly, possession of a fully reflecting mirror was an excommunicable offence for members of the Thorn-God’s congregation.
8. The story is believed to refer to the execution of a nobleman called Yokh-Tsiolphë (Yugg-Siurphë in some texts), who had offended the Queen either by refusing to sacrifice his eldest son and daughter to the Thorn-God or (as most scholars now believe) by falling under suspicion of having composed an anonymous pasquinade against the Thorn-God which was briefly circulated at the royal court in 38 A.D./1174 A.S.I. The execution would have been one of the earliest signs of the Queen’s growing regard for the Thorn-God.
9. The Yihhian here is a little unclear and the reference is perhaps to the Osprey (Pandion haliætus), which was second only to the Great Grey Shrike (Lanius excubitor) in the ornithomancy of the Temple.
10. The Yihhian kiuthi literally means “spotted one” and can refer to several species of animal; “leopard” seems the most appropriate translation in this context.
11. Niédýthithlà (mhló)Nhriúlr, literally “deathly lord(’s)”, was a title of the Thorn-God, but the foreign derivation of the words in Yihhian means it is perhaps best translated into English as “thanatocrator”.
12. Blossoms of gorse (Ulex spp) and other spinose plants were thrown beneath the feet of dancing priests during rituals at the Temple, and many of the Temple’s hymns refer to osmomancy, or divination by the scents released from the crushed petals.
13. She is said to have been planning another round of the puerile and puellar sacrifices with which she purchased her unnatural youth at the time of her death, occasioned when she slipped on trampled petals in the Temple of the Thorn-God whilst approaching the altar for blessing and was impaled on the silver thorns topping a newly erected altar-rail. Some contemporary commentators hinted at numerological significance in her death, saying that the priests of the Thorn-God had persuaded her that by laying down her life at that age she would regain it at the beginning of the next cosmic cycle. It is possible, therefore, that the encephalotomy and cardiotomy of her ritual mummification were feigned.
Aivazovsky was a citizen of Imperial Russia whose name is Հովհաննես Այվազյան in Armenian and Иван Айвазовский in Russian.
«Il vino è la luce del sole tenuta insieme dall’acqua.» — Galileo (1564-1642)
“Wine is sunlight held together by water.” — Galileo
The most powerful drug in the world is water. The second most powerful is language. But everyone’s on them, so nobody realizes how powerful they are. Well, you could stop drinking water. Then you’d soon realize its hold on the body and the brain.
But you can’t stop using language. Try it. No, the best way to realize the power of language is to learn a new one. Each is a feast with different flavours. New alphabets are good too. The Devanagari alphabet is one of the strongest, but if you want it in refined form, try the phonetic alphabet. It will transform the way you see the world. That’s because it will make you conscious of what you’re already subconsciously aware of.
But “language” is a bigger category that it used to be. Nowadays we have computer languages too. Learning one is another way of transforming the way you see the world. And like natural languages – French, Georgian, Tagalog – they come in different flavours. Pascal is not like Basic is not like C is not like Prolog. But all of them seem to put you in touch with some deeper aspect of reality. Computer languages are like mathemagick: a way to give commands to something immaterial and alter the world by the application of will.
That feeling is at its strongest when you program with machine code, the raw instructions used by the electronics of a computer. At its most fundamental, machine code is simply a series of binary numbers controlling how a computer processes other binary numbers. You can memorize and use those code-numbers, but it’s easier to use something like assembly language, which makes machine-code friendlier for human beings. But it still looks very odd to the uninitiated:
That’s almost at the binary bedrock. And machine code is fast. If a fast higher-level language like C feels like flying a Messerschmitt 262, which was a jet-plane, machine-code feels like flying a Messerschmitt 163, which was a rocket-plane. A very fast and very dangerous rocket-plane.
I’m not good at programming languages, least of all machine code, but they are fun to use, quite apart from the way they make you feel as though you’re in touch with a deeper aspect of reality. They do that because the world is mathematics at its most fundamental level, I think, and computer languages are a form of mathematics.
Their mathematical nature is disguised in a lot of what they’re used for, but I like to use them for recreational mathematics. Machine-code is useful when you need a lot of power and speed. For example, look at these digits:
1, 2, 3, 4, 5, 6, 7, 8, 9, 1*, 0*, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6*, 3*, 7, 3, 8, 3, 9, 4, 0, 4, 1, 4, 2, 4…
They’re what the Online Encyclopedia of Integer Sequences (OEIS) calls “the almost natural numbers” (sequence A007376) and you generate them by writing the standard integers – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13… – and then separating each digit with a comma: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3… The commas give them some interesting twists. In a list of the standard integers, the 1st entry is 1, the 10th entry is 10, the 213rd entry is 213, the 987,009,381th entry is 987,009,381, and so on.
But that doesn’t work with the almost natural numbers. The 10th entry is 1, not 10, and the 11th entry is 0, not 11. But the 10th entry does begin the sequence (1, 0). I wondered whether that happened again. It does. The 63rd entry in the almost natural numbers begins the sequence (6, 3) – see the asterisks in the sequence above.
This happens again at the 3105th entry, which begins the sequence (3, 1, 0, 5). After that the gaps get bigger, which is where machine code comes in. An ordinary computer-language takes a long time to reach the 89,012,345,679th entry in the almost natural numbers. Machine code is much quicker, which is why I know that the 89,012,345,679th entry begins the sequence (8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9):
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 63, 3105, 43108, 77781, 367573, 13859021, 77911127, 911360799, 35924813703, 74075186297, 89012345679…
And an ordinary computer-language might give you the impression that base 9 doesn’t have numbers like these (apart from the trivial 1, 2, 3, 4, 5, 6, 7, 8, 10…). But it does. 63 in base 10 is a low-hanging fruit: you could find it working by hand. In base 9, the fruit are much higher-hanging. But machine code plucks them with almost ridiculous ease:
1, 2, 3, 4, 5, 6, 7, 8, 10, 570086565, 655267526, 2615038272, 4581347024, 5307541865, 7273850617, 7801234568…
Papyrocentric Performativity Presents:
• Nature by Numbers – 30-Second Elements: The 50 Most Significant Elements, Each Explained in Half a Minute, ed. Eric Scerri (Icon 2013)
• Fresh Flesh – The Complete Illustrated Guide to Freshwater Fish & River Creatures, Daniel Gilpin and Dr Jenny Schmid-Araya (Hermes House 2011)
• The Reich Stoff – Rocket and Jet Aircraft of the Third Reich, Terry C. Treadwell (Spellmount 2011)
• Past Masters – Justice for All: The Truth about Metallica, Joel McIver (Omnibus Press, revised edition 2014)
• Ant on E – Burgess on Waugh
• M.O.R. of Babylon – Sleazy Listening: Frottage, Fladge and Frenzied Fornication in the Music of the Carpenters, Dr Miriam B. Stimbers (University of Nebraska Press 2015)
Or Read a Review at Random: RaRaR