Tuesday, December 24, 2024

Quincunx

Quincunx (pronounced kwing-kuhngks or kwin-kuhngks)

(1) An arrangement of five objects, in a square or rectangle, one at each corner and one in the middle.

(2) In formal gardening, five plants placed thus as part of a design,

(3) In forestry, as a baseline pattern, five trees planted in such a shape.

(4) In botany, an overlapping arrangement of five petals or leaves, in which two are interior, two are exterior, and one is partly interior and partly exterior (described as a “quincuncial arrangement” of sepals or petals in the bud.

(5) The pattern of the five-spot on dice, playing cards and dominoes.

(6) In the history of numismatics, a bronze coin minted during the Roman Republic, valued at five-twelfths of an as (five times the value of the uncia); it was marked with five dots.

(7) In geometry, an angle of five-twelfths of a circle.

(8) In astrology An angle of five-twelfths of a circle (or 150°) between two objects (usually planets).

1640s: From the Latin quīncunx (the basis for the construct being quīnque + uncia) which translates literally as five twelfths”, a reference to a bronze coin minted (circa 211–200 BC) with a five dot pattern and issued by the Roman Republic; it was valued at five twelfths of an as (the Roman standard bronze coin).  Descendants from the Latin include the English quincunx, the French quinconce, the German Quinkunx, the Spanish quincunce and the Portuguese quincunce.  Quinque (the numeric five (5)) was from the From Proto-Italic kwenkwe, from the primitive Indo-European pénkwe, the cognates including the Sanskrit पञ्चन् (páñcan), the Ancient Greek πέντε (pénte), the Old Armenian հինգ (hing), the Gothic fimf and the Old English fīf (from which English ultimately gained “five”).  The basis of the construct of the Latin uncia may have been ūnicus (unique) (from ūnus (one), from the primitive Indo-European óynos) in the sense of twelfths making up the base unit of various ancient systems of measurement) + -ia.  Not all etymologists agree and some prefer a link with the Ancient Greek γκία (onkía) (uncia), from γκος (ónkos) (weight).  Uncia was the name of various units including (1) the Roman ounce (one-twelfth of a Roman pound), (2) the Roman inch (one-twelfth of a Roman foot), (3) a bronze coin minted by the Roman Republic (one-twelfth of an as), (a Roman unit of land area (one-twelfth of a jugerum)) and in the jargon of apothecaries became a synonym of ounce (the British & American avoirdupois unit of mass); it was generally a synonym of twelfth.  In algebra, it was a (now obsolete) numerical coefficient in a binomial.  Quīnque was the source of many modern Romance words for “five” including the French cinq and the Spanish cinco; uncia was the source of both “inch” and “ounce”.  Quincunx is a noun, quincuncial is an adjective and quincuncially is an adverb; the noun plural is quincunxes or quincunces.

Quincunx garden, Wyken Hall, Suffolk, England.

When first it entered English in the 1640s, “quincunx” existed only in the vocabulary of astrologers (astrology then still a respectable science) and it was used to describe planetary alignments at a distance of five signs from one another.  By the 1640s it had migrated to mathematics (particularly geometry) where it was used to define “an arrangement of five objects in a square, one at each corner and one in the middle”, familiar in the five pips on a playing card or spots on a di).  In the 1660s (possibly from dice or cards rather than the fortune-tellers), it was picked up by gardeners to describe the layout of a section of a formal garden in which one plant or shrub was placed at each corner of a square or rectangle with a fifth exactly in the centre (an arrangement in two sets of oblique rows at right angles to each other, a sense known also in the original Latin.  In forestry, use began (as a layout tool for new plantings) early in the eighteenth century.

Lindsay Lohan (born 2 July 1986) joins a list of the illustrious with a Mercury Quincunx MC (a planetary alignment where Mercury is 150o apart from the Medium Coeli (a Latin phrase which translates as “Midheaven” (“MC” in the jargon of astrologers).  In explaining the significance of the Quincunx MC, the planetary soothsayers note than when two planets lie 150o apart, “tension is created due to their lack of natural understanding or relation.  The MC is the point where the cusp of the tenth house is found on a natal (birth) and the MC sign signifies  one’s public persona.  Now we know.

Fluffy dice in 1974 Ford Mustang II (left), the color of the dashboard molding emblematic of what was happening in the 1970s.    In continuous production over seven generations since 1964, the Mustang II (1973-1979) is the least fondly remembered iteration (uniquely among Mustangs, in its first season a V8 engine was not even optional) but, introduced some weeks before the first oil embargo was imposed in 1973, it was a great sales success and exceeded the company’s expectations.  Unlike at least some of the models in all other generations, the Mustang II is a classic “Malaise era” car and not a collectable in the conventional sense of the word although they do have a residual value because the front sub-frame with its rack & pinion steering and flexible engine accommodation is prized for all sort of purposes and many have been cannibalized for this assembly alone.  Fluffy dice are available also in designer colors (right) and as well as the familiar dots, there are some with hearts, skulls, handguns, eyes and dollar signs.  Probably, the Mustang II and fluffy dice are a perfect match.

Although the five-dot pattern on a di is known in the industry as the quincunx, the other five faces enjoy rather more prosaic descriptions and most just use the number:

1 (single dot, at the center of the face): The “center dot” or “monad”.

2 (two dots, diagonally opposite each other): The “diagonal pair”.

3 (three dots, forming a diagonal line): The “diagonal trio”.

4 (four dots, arranged in a square pattern: The “square” or “quadrant”.

6 (six dots, arranged in two parallel vertical lines of three dots each): The “double row” or “paired trios”.

US Army five star insignia of (General of the Army) Dwight Eisenhower (1890-1969; US president 1953-1961).

The quincunx was one of the layouts considered in 1944 when, for the first time, the US military created five star ranks in the army and navy (there would not be a separate USAF (US Air Force) until 1947).  Eventually a pentagrammatic circle of stars was preferred but the aesthetics of epaulettes were the least of the problems of protocol, the military been much concerned with history and tradition and the tangle wasn’t fully combed out until 1976 when the Congress, the White House, and the Pentagon, acting in succession, raised George Washington (1732–1799; first president of the United States, 1789-1797) to the rank of five star general (he’d retired as a (three star) lieutenant general), back-dating the appointment so he’d for all time be the military’s senior officer.  In 1944, there was also an amusing footnote which, according to legend, resulted in the decision to use the style “general” and not “Marshal” (as many militaries do) because the first to be appointed was George Marshall (1880–1959; US Army chief of staff 1939-1945) and it was thought “Marshal Marshall” would be a bit naff, something Joseph Heller’s (1923-1999) “Major Major” in Catch-22 (1961) would prove.

The quincunx induction system, the Cadillac Le Monstre and the 24 Heures du Mans, 1950

Living up to the name: The 1950 Cadillac Le Monstre.

The two Cadillacs which in 1950 raced at Le Mans were mechanically similar but visually, could have been from different planets.  The more conventional Petit Pataud was a Series 61 coupe with only minor modification and it gained its nickname (the translation “clumsy puppy” best captures the spirit) because to the French it looked a lumbering thing but, as its performance in the race would attest, Cadillac’s new 331 cubic inch (5.4 litre) V8 (which would grow to 429 cubic inches (7.0 litres) before it was retired in 1967) meant it was faster than it looked.  Underneath the second entrant (Le Monstre obviously needing no translation but used in the sense of “monstrosity” rather than “large”) there was also a Series 61 but the body had been replaced by something more obviously aerodynamic although few, then or now, would call it “conventionally attractive”.  Although Le Monstre seemed very much in the tradition of the “cucumber-shaped” Mercedes-Benz SSKL which had won the 1932 race at Berlin’s unique AVUS circuit, the lines were the result of testing a one twelfth (Uncia in the Latin) scale wooden model in a wind-tunnel used usually to optimize the shape crop dusters and other slow-flying airplanes.  Presumably that explains the resemblance to a section of an airplane’s wing (a shape designed to encourage lift), something which would have been an issue had higher speeds been attained but even on the long (6 km (3.7 mile)) Mulsanne Straight, there was in 1950 enough power only to achieve around 210 km/h (130) mph although as a drag-reduction exercise it must have contributed to the 22 km/h (13 mph) advantage it enjoyed over Petit Pataud, something Le Monstre’s additional horsepower alone could not have done and remarkably, even with the minimalist aluminium skin it wasn’t much lighter than the standard-bodied coupe because this was no monocoque; the robust Cadillac chassis was retained with a tube-frame added to support the panels and provide the necessary torsional stiffness.

Le Monstre's 331 cubic inch V8 with its unusual (and possibly unique) five-carburetor induction system in a quincunx layout.

Some of the additional horsepower came from the novel "quincunx" induction system.  Le Monstre’s V8 was configured with five carburettors, the idea being that by use of progressive throttle-linkages, when ultimate performance wasn’t required the car would run on a single (central) carburettor, the other four summoned on demand and in endurance racing, improved fuel economy can be more valuable than additional power.  That’s essentially how most four-barrel carburettors worked, two venturi usually providing the feed with all four opened only at full throttle and Detroit would later refine the model by applying “méthode Le Monstre” to the triple carburettor systems many used between 1957-1971.  As far as is known, the only time a manufacturer flirted with the idea of a five carburetor engine was Rover which in the early 1960s was experimenting with a 2.5 (153 cubic inch) litre in-line five cylinder which was an enlargement of their 2.0 litre (122 cubic inch) four.  Fuel-injection was the obvious solution but the systems then were prohibitively expensive (for the market segment Rover was targeting) so the prototypes ended up with two carburettors feeding three cylinders and one the other two, an arrangement as difficult to keep in tune as it sounds.  Rover’s purchase of the aluminium 3.5 litre (214 cubic inch) V8 abandoned by General Motors (GM) meant the project was terminated and whatever the cylinder count, mass-produced fuel injection later made any configuration possible.  Five carburettors wasn’t actually the highest count seen in the pre fuel-injection era, Ferrari and Lamborghini both using six (done also by motorcycle manufacturers such as Honda and Benelli) and Moto-Guzzi in the 1950s fielded a 500 cm3 Grand-Prix bike with the memorable component count of 8 cylinders, 4 camshafts, 16 valves & 8 carburetors.  The early prototypes of Daimler’s exquisite hemi-head V8s (1959-1969) were also built with eight carburettors because the original design was based on a motorcycle power-plant, the reason why they were planned originally as air-cooled units.

Le Monstre ahead of Petit Pataud, Le Mans, 1950.  At the fall of the checkered flag, the positions were reversed. 

Motor racing is an unpredictable business and, despite all the effort lavished on Le Monstre, in the 1950 Le Mans 24 hour, it was the less ambitious Petit Pataud which did better, finishing a creditable tenth, the much modified roadster coming eleventh having lost many laps while being dug from the sand after an unfortunate excursion from the track.  Still, the results proved the power and reliability of Cadillac’s V8 and Europe took note: over the next quarter century a whole ecosystem would emerge, crafting high-priced trans-Atlantic hybrids which combined elegant European coachwork with cheap, powerful, reliable US V8s, the lucrative fun lasting until the first oil crisis began in 1973.

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