Diagonal

Diagonal (pronounced dahy-ag-uh-nl or di-ag-nl (both uses U & non-U)

(1) In mathematics, connecting two nonadjacent angles or vertices of a polygon or polyhedron, as a straight line.

(2) In mathematics, a set of entries in a square matrix running either from upper left to lower right (main diagonal, or principal diagonal ) or lower left to upper right (secondary diagonal ).

(3) In number theory, as the broken diagonal, in the theory of magic squares, a set of n cells forming two parallel diagonal lines in the square.

(4) In linear algebra, as diagonal matrix, a matrix in which the entries outside the main diagonal are all zero.

(5) In geometry, extending from one edge of a solid figure to an opposite edge, as a plane (joining two nonadjacent vertices).

(6) In category theory, as diagonal morphism, a morphism from an object to the product of that object with itself, which morphism is induced by a pair of identity morphisms of the said object.

(7) Something with or assuming an oblique direction; having slanted or oblique lines or markings; having a slanted or oblique direction.

(8) In typography, a virgule (a slash), known also as a solidus (used in computing file systems variously as forward slash & back slash or slash & slosh (the generalized term the diagonal mark).

(9) In design, any line or pattern using diagonals; something put, set, or drawn obliquely.

(10) In fabrics, a cloth marked or woven with slanting lines or patterns

(11) In manège, of a horse at a trot, the state in which the foreleg and the hind leg, diagonally opposite, which move forward simultaneously.

(12) In zoological anatomy, of or related to the cater-corner (diagonally opposite) legs of a quadruped, whether the front left and back right or front right and back left.

(13) In chess, one of the oblique lines of squares on a chessboard (the mode in which a bishop may be moved).

1400s: From the Middle French diagonal From the Latin diagōnālis, the construct being the Ancient Greek διαγώνιος (diagṓn(ios)) (from angle to angle) + the Latin -ālis (the third-declension two-termination suffix (neuter -āle) used to form adjectives of relationship from nouns or numerals).  The construct of the Greek diagōnios, was dia- + γωνία (gōnía) (angle; corner), from the primitive Indo-European root genu- (knee; angle).  The dia- prefix was from the Ancient Greek prefix δια- (dia-), from διά (diá) (through, across, by, over) and was most productive, the familiar forms including diadem, diacritical, diagnosis, diagram, diameter, dialect, dialogue & diatribe.  The adjective diagonal (implied in diagonally) (extending as a line from one angle to another not adjacent) dates from the early fifteenth century and was from the Old French diagonal, from the Latin diagonalis, from diagonus (slanting line), from the Ancient Greek diagōnios.  It emerged as a noun in the 1570s in the sense of “a straight line drawn from one angle to or through another not adjacent, in a plane or solid figure".  The specific technical meaning in chess describes "a line of squares running diagonally across a board" and is the mode in which a bishop may move).  Diagonal is a noun & adjective, diagonality is a noun and diagonally is an adverb; the noun plural is diagonals.

Defying the tyranny of the horizontal line: Lindsay Lohan’s hand-written notes made during one of her court appearances in Los Angeles, July 2010.  Even on the Reddit subs where exist the planet’s most unforgiving critics, most were so taken with the neatness of the lettering, the diagonality attracted barely a comment.

A diagonal measurement is defined usually by describing a line between the bottom left and the upper right corners (or vice versa) of a square or rectangle.  It has a nuanced value when used of computer monitors, televisions and such because it has to be read in conjunction with the aspect ratio of the device.  A 19 inch (monitor sizes usually expressed in inches although the French will always include a metric conversion) monitor in a 16:9 aspect will be very different from a 19 inch 4:3 device.  In computing, what began in typography, as diagonal marks (the virgule (often called a slash of solidus (/) and the later “back slash (\)) are used in computing file systems to separate directories & sub-directories (now familiar as folders) from file names.  Under MS/PC-DOS, OS/2 & Windows, a file called myfile.txt to a sub-directory called text in a directory called user on D: drive would be displayed in the path D:\user\text\myfile.txt (although under DOS it would be in upper case).  The Windows crowd call these diagonal marks “back slashes” and the solidus they call “forward slashes” and they’re used for other purposes.  The Unix crew think this childish and insist a solidus is a “slash” and there’s no such thing as a back-slash which real people call a slosh.

Notable moments in diagonal (canted) headlamps

The one-off, 1938 Jaguar SS100 fixed head coupé (FHC) “Grey Lady” which demonstrates the traditional placement when four lights were used.

The inclination designers for decades felt to use a diagonal arrangement for headlights began innocently enough in the pre-war years when it emulated the usual practice of placing a pair of driving lamps or for lights inboard of the main headlamps and lower down, mounted typically on the bumper bar or its supporting brackets.  Most headlamps until the late 1930s were in separate housings, as were the auxiliary devices and even cars which integrated them into the coachwork adopted the same geometry.  This was due in part to the evolutionary nature of automobile styling which has often tried to avoid the “shock of the new” and in part to regulations, especially those which applied in the US.

Jaguar S-Type (1963-1968, left), Vanden Plas Princess R (1964-1968, centre) and Volvo 164 (1968-1975, right).

Although most would regard the technique which essentially integrated the driving lamps/fog lamps into the coachwork as just a variation on the diagonal theme, professional designers insist not; they say this is just wrapping enveloping bodywork around an existing device.  Also, the professionals prefer the term “canted headlamps” because “diagonal” has a more precise definition in mathematics.

Rover 3.5 Coupé (P5B 1967-1973, left) and Packard Coupe (1958) (right)

While the US manufacturers usually re-tooled in 1957-1958 after regulations had been changed to allow quad head-lamps, the British were often fiscally challenged and needed to continue to use existing sheet metal.  A design like the Vanden Plas Princess R (and the companion Wolseley 6/99 & 6/110 (1959-1968)) has sufficient space to allow the diagonal placement but the Rover P5 (1958-1967) with its wider grill precluded the approach so the expedient solution was to go vertical.  Although obviously just “bolted on”, such was the appeal of the P5B it just added to the charm.  It could have been much worse because less charming was the 1958 Packard Coupe, produced by Studebaker-Packard, the company an ultimately doomed marriage of corporate convenience which seemed at the time a good idea but proved anything but. Studebaker-Packard lacked the funds to re-tool to take advantage of the rules allowing four head-lamps but without the feature their cars would have looked even more hopelessly outdated than they anyway did so cheap fibreglass “pods” were produced which looked as “tacked on” as they were.  They were the last Packards made and Studebaker’s demise followed within a decade.

1963 Zunder

The Zunder ("spark" in German) was produced in Argentina between 1960-1963 and used the power-train from the Porsche 356.  The body was fashioned in fibreglass and was one of the many interesting products of the post war industry in Brazil and Argentina, the history of which is much neglected.  By the standards of time, it was well-built but as a niche product, was never able to achieve the critical mass necessary to ensure the company’s survival and production ceased in 1963 after some 200 had been built.

Buick Electra 225 (First generation 1959–1960, left) and (Lincoln) Continental Mark III (1958-1960, right).  The Buick adopted horizontal headlamps in 1960.

In the late 1950s, most US manufacturers did have cash to spend and the industry spirit at the time was never to do in moderation what could be done in excess although by comparison with the Lincoln, the Buick verged on the restrained.  Tellingly, the Buick sold well while the Continental was such a disaster Ford considered sending Lincoln to join Edsel on the corporate scrapheap and the nameplate was saved only because it was possible at low cost to re-purpose a prototype Ford Thunderbird as the new Continental.  Rarely has any replacement been such a transformation and the 1961 Continental would influence the design of full-sized American cars for twenty years.  It used horizontally mounted head-lamps.

1961 Chrysler 300 G.

Chrysler’s “Letter Series 300” (1955-1965) coupes and convertibles were the brightest glint in the golden age in which Detroit’s power race was played out in the big cars, an era which would be ended by the introduction of the intermediates and pony cars in the 1960s.  The 300G (1961) was visually little changed from the previous year’s 300F but the simple change to diagonal headlamps was transformative.  There were those who didn’t like the look but generally it was well received and as a first impression, the feeling might have been Chrysler had mastered the motif in a way the Continental Mark III proved Ford just didn’t get it.

1961 DeSoto Adventurer (left), 1962 Dodge Dart (centre) and 1963 Dodge Polara (right).

However, Chrysler’s designers in the early 1960s may have decided they liked diagonal headlamps which was good but seemingly they liked them so much they though the buyers should be offered as many permutations of the idea as could be made to work on a production line.  What’s remarkable is not that the public didn’t take to the approach but that it took the corporation so long to admit the mistake and try something more conventional.  Just to hedge their bets, while Dodge, Plymouth and DeSoto all had headlamps mounted at an obvious degree of cant, on the Chryslers the effect was so subtle one really needed to hold a spirit level to the front end to confirm there was an slant, albeit one imperceptible to the naked eye.  The one division which never were the diagonal way was the Imperial but it’s headlamp treatment was more bizarre still.

1961 DeSoto styling proposal (September 1958) for the 1961 range.

For DeSoto, things could have looked worse even than they did, some of the implementations of the diagonal motif which went as far as clay models or actual metal prototypes so bizarre one wonders what external influences were being studied (or inhaled).  As it turned out, 1961 would be the end of the line for DeSoto, a nameplate which had been successful as recently as the mid 1950s.  Its demise was little to do with diagonal head-lamps (though they didn’t help) but a product of Chrysler’s other divisions expanding their ranges up and down, encroaching on a market segment DeSoto once found so lucrative.  The phenomenon was a harbinger of the eventual fate of marques like Mercury, Pontiac, Oldsmobile and Plymouth.

Clockwise from top left: Fiat 8V (1952-1954), Gordon-Keeble GK-1 (1961-1967), Jensen C-V8 (1962-1966) and Triumph Vitesse (1962-1971).

Perhaps surprisingly, the French majors were never enamored, presumably because Citroën and Renault didn’t like to be imitative and Peugeot were too conservative.  Some of the Europeans did dabble with the idea, embracing it as an expression of modernity although the then radical treatment of the head-lamps sometimes struck a discordant note when they were grafted onto something where the rest of the platform was so obviously from one or two generations past.  Fiat’s exquisite 8Vs didn’t all get the diagonal look but those which did remain the most memorable of the few of the breed built.  An unqualified aesthetic success was the Gordon-Keeble built to aviation standards and powered by a Chevrolet V8.  It deserved to succeed but floundered as much of the British industry did in the era because of a lack of capitalization and an accounting operation which didn’t match the quality of the Engineering.  More successful was the Jensen C-V8 but while the distinctive front end now makes it much prized by collectors, at the time it was less admired and its very presence served only to emphasize how antiquated the rest of the styling had become.  For its replacement, Jensen tuned to an Italian styling house and the Interceptor, introduced in 1966 and remembered for the vast expanse or rear glass, is now thought a classic of the era.  The one which sold best was the Triumph Vitesse, one of a number of variations built on the robust and versatile separate chassis of the Herald (1959-1971) including the Spitfire and GT6.  Somewhat the BMW M3 of its day, the Vitesse’s front end actually lived on in India (though without the lusty six cylinder engines) but curiously, the inner headlights weren’t fitted.

Gilding the lily: The Lancia Fulvia coupé (1965-1976) before & after.

The lovely, delicate lines of the Lancia Fulvia were perfect and really couldn’t be improved.  The unfortunate facelift with the canted lights was no improvement.

Ogee

Ogee (pronounced oh-jee)

(1) A double curve, resembling the letter S, consisting of two arcs that curve in opposite directions so that the ends are parallel.   An ogee is a kind of sigmoid curve, technically formed by the union of a concave and a convex line.

(2) In architecture, a molding with such a curve for a profile; cyma, also called gula or talon.

(3) In fluid mechanics, a specific aerodynamic profile.

(4) In mathematics, an inflection point.

(5) In cosmetic surgery, a desired shape for the curve of the malar or cheekbone prominence transitioning into the mid-cheek hollow.

(6) In distillation, the bubble-shaped chamber of a pot still connecting the swan neck to the pot which allows distillate to expand, condense and fall back into the pot.

1275-1325: From the Middle English ogeus (plural oggez), ogeve, egeve & egeove, variants by assimilation from the French oggif (diagonal rib of a vault) from the Old French œgive, ogival, ogive & augive, from the Late Latin augiva of uncertain origin.  In the Late Latin there was ogis (a support, prop), thought derived from the Classical Latin augeō (to increase, strengthen) from which Spanish gained auge (highest point of power or fortune; apogee); a doublet of ogive.  The use in architecture to describe regular & irregular S-shaped moldings began in the 1670s, supplanting the earlier augive, from the Late Latin augiva of uncertain origin but perhaps related to the Latin via (way; road).  In the Middle English, the late thirteenth century ogif was "a stone for the diagonal rib of a vault", derived from the French and the Medieval Latin ogiva.

An Ogee arch.

An ogee is a curved shape vaguely like an “S”, consisting of two arcs that curve in opposite senses, so that the ends are tangential.  In architecture, it’s used to describe a molding with a profile made by a lower concave arc flowing into a convex arc.  Used first in Persian and Greek architecture from Antiquity, it’s most familiar now as a part of the Gothic style.  Because the upper curves of the ogee arch are reversed, it’s not suitable where the load-bearing rates are high and it’s thus used mostly in self-supporting structures exposed to their own weight and not subject to high external forces.

An inflection point.

In mathematics, an ogee is an inflection point, a point on a curve at which the sign of the curvature (ie the concavity) changes; inflection points may be stationary but are neither local maxima nor local minima.  Inflection Points merely mark the point on the curve where it changes from concave upward to concave downward (or vice versa), it is not a directional measure.  Calculus is needed to find where a curve goes from concave upward to concave downward and for this mathematicians use derivatives, one which determines the slope and a second which defines whether the slope increases or decreases.

The cosmetic surgeon's template.

When cosmetic surgeons speak of the ogee curve, they’re referring to the elongated S curve which, when looking at a patient’s face at a three-quarter aspect, describes the curve from the eye through the cheek down to below the cheek (technically the malar or cheekbone prominence transitioning into the mid-cheek hollow).  As people age, the face loses volume in our face and the ogee curve flattens out. With facelifts and related procedures, the cosmetic surgeon aims to create an ogee curve, restoring the chiseled refinement of youth.

Lindsay Lohan, Cosmopolitan, October 2022 edition (photographs by Ellen Von Unwerth (b 1954)).  The photographs illustrate the ideal ogee curve in the facial structure and Ms Lohan shows how a model's pout can be used to optimize the effect.  The car is a second generation AMC Javelin (1971-1974).

Shapes derived from the ogee curve are popular design motifs used for just about everything where they can be applied but it's most associated with large, flat surfaces because it's in such spaces the geometric repetition can be most effective, thus the prevalence in fabrics, wallpaper and floor-coverings.  The mind visualizes the shape as something like a two-headed onion and it's probably the association with the architectural style so often seen on mosques or other structures in the Arab world that in there's presumed to be some Islamic influence but ogee long pre-dates Islam.  There are few conventions of use except that the designs tend to be displayed in either a horizontal or vertical aspect; diagonal deployment is rare.

In fluid mechanics, the ogee describes the shape used to create certain aerodynamic profiles, the classic example being the delta wing of the Concorde airplane.  The ogee-type wing used on the Concorde one flavor of the compound delta (sometimes called double delta or cranked arrow) where the leading edge is not straight.  Typically the inboard section has increased sweepback, creating a controlled high-lift vortex without the need for a foreplane and the shape of the sweepback is defined by the parameters of the ogee.  On the Concorde, the two sections and cropped wingtip merge into a smooth ogee curve.

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 ὀγκία (onkía) (uncia), from ὄγκος (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 150^o 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 150^o 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.

Catawampus

Catawampus (pronounced kat-uh-wom-puhs)

(1) Out of alignment, in disarray or disorder; crooked, askew, awry.

(2) Positioned diagonally; cater-cornered; obliquely.

(3) Of fierce demeanor or appearance (archaic).

1830s: A US colloquialism which originally meant “utterly” or “of fierce demeanor or appearance”, apparently influenced by (wild)cat + rumpus or the fierce looking catamount (cougar, puma, lynx).  As a noun, the US use described “a fierce imaginary animal, a bogeyman”.  The rapid meaning shift to “positioned diagonally” (which influenced the later use to mean “askew; awry” is explained by the construct being cata- (diagonally (from cater-cornered)) + -wampus.  The alternative spellings recorded include caddywompus, caliwampus, caliwampous, cankywampus catawamptious and (influenced by cat, catty, kitty) cattywampus, catiwampus, cattywampous; kittywampus, kittywumpus.  The synonyms include askew, awry, crooked, off-kilter, skewampus & skiwampus.  Catawampus is an adjective & adverb (and historically a noun); the noun plural was catawampuses.

Kitty corner.

The term “cater-cornered” dates from the early nineteenth century and has an archaic feel but is still in use variously as kitty-cornered, catty-cornered & caddy-cornered, depending on the region; catty-corner is the form most often used in the UK while kitty-corner prevails in North America and although it’s rare anywhere, caddy-corner seems to know no boundaries.  It has nothing to do with felines and refers to something which lies in a position diagonally across from something else and can be applied to streets, rooms, or any other space or place where the requisite corners exist.  As a descriptor of location, it’s dependent not on proximity but the diagonality of the relationship; a building might be within a few feet of the one beside or on the opposite side of the street but to be catty-cornered, it need not be all that close, just in the right place.

Catawampus: At this intersection, buildings one & four and buildings two & three are catawamptic and thus catty or kitty cornered.

Catty-cornered is said to have been the original version, from the French quatre (four), meaning four.  Quatre was from the Old French quatre, qatre & catre, from the Latin quattuor, from the primitive Indo-European ketwóres and was picked up by a number of European languages including the Catalan quatre, the Italian quattro, the Portuguese quatro and the Spanish cuatro.  In English, quatre became cater, used to showcase the four spots on a die or the four legs of a beast and, as cater-cornered, the four corners created where two streets cross.  From here, the term evolved to describe the buildings positioned diagonally from each-other on those corners, like the opposite corners on a square die.  Then, cater-cornered evolved as catty-corner, kitty-corner and caddy-corner, something not uncommon at a time when regionalisms were much more common.  Wampus was US slang for a lout or yokel but the use may have been a corruption of the archaic Scottish wampish which, when used as an intransitive verb, meant “to wriggle, twist, swerve or flop about (a la a swimming fish).

Catawampic mug shots; the concept able to be applied to just about any diagonal relationship: Here, Lindsay Lohan & Donald Trump are kitty-cornered and Bill Gates & Rudy Giuliani are kitty-cornered.

Some sources suggest the earliest use appears to have been the adverbial catawampusly (1834) which expressed no specific meaning but was an intensifier meaning “utterly, completely; with avidity, fiercely, eagerly”.  The noun as catawampus dates from 1843 when it was used as a name for an imaginary hobgoblin, a fierce imaginary animal or a bogeyman (and even a sense of fright), perhaps from influence of catamount (cougar, puma, lynx).  The adjective was used since the 1840s as an intensive but etymologists caution the use was almost exclusively in British publications lampooning the Americanisms in US English.  By 1864 it has come to mean “askew, awry, wrong” but the regionalism which most spread was that in North Carolina (dating from 1873) which meant “in a diagonal position, on a bias, crooked” and that persists to this day.  This orthodox etymology is generally accepted but because documentary evidence of the origin is lacking, it really is all speculative and etymologists note catawampus may well have been one of the many jocular, pseudo-classical formations popular in the slang of mid-nineteenth century America.

Trends of use of "kitty-corner" & "catty-corner" in the US, one of a series of statistical representations by Joshua Katz, Department of Statistics, North Carolina State University.  Catty-corner is the preferred form south of the Mason-Dixon Line but it fades from use in Florida, reflecting presumably the inward migration pattern from the northern states.

Signature

Signature (pronounced sig-nuh-cher or sig-nuh-choor)

(1) A person's name, or a mark representing it, as signed personally or by deputy, as in subscribing a letter or other document.

(2) The act of signing a document.

(3) In music, a sign or set of signs at the beginning of a staff to indicate the key or the time of a piece.

(4) In broadcasting, a song, musical arrangement, sound effect, etc., used as a theme identifying a program.

(5) Any unique, distinguishing aspect, feature, or mark.

(6) In computing, as digital signature, any one of a number of attempts to create a mechanism whereby a digital object can have the same unique identifying characteristic as a physical signature in ink; in cryptography, data attached to a message certifying the message originated from its claimed source; in email and some other variations of communication, test, images or other objects collectively appended usually at the end of a message, analogous with a traditional signature on a letter.

(7) In digital forensic analysis, as digital signature, a term used to refer to any collection of characteristics which can be used as an identifier of origin, intent etc;

(8) The part of a prescription for pharmaceuticals instructing the patient the frequency and quantity in which a drug should be administered (US only).

(9) As an adjective, something intended to be emblematic of an institution or individual (signature dish signature cocktail, signature scent etc).

(10) In printing, a sheet of paper printed with several pages that upon folding will become a section or sections of a book; such a sheet so folded.

(11) In mathematics, a tuple specifying the sign of coefficients in any diagonal form of a quadratic form.

(12) In medicine, a resemblance between the external character of a disease and those of some physical agent (obsolete).

1525-1535: From the Old & Middle French signature, from the Medieval Latin signātura, future active periphrastic of the verb signāre (to sign), the construct being signum (sign), + -tura, feminine of -turus, the future active periphrastic suffix.  The first use with a link to English appears to have been as a kind of document defined in Scottish law.  The Medieval Latin signatura, was, in Classical Latin a rescript (the matrix of a seal).  The meaning "one's own name written in one's own hand" is from 1570s, which replaced the early-fifteenth century “sign-manual” in this sense.  The use in musical notation in which composers used "signs placed it the beginning of a staff to indicate the key and rhythm" was noted first in 1806.  Signature began to be used in the generalized sense of "a distinguishing mark of any kind" as early as the 1620s.

Non est factum

Historically, in contract law a signature was binding on the party who signed and obliged the performance of the specific terms of the contract.  Even if someone could prove they signed because of their own misunderstandings or in an act of carelessness even to the point of gross negligence, courts would still usually enforce the contract but a notable exception was the doctrine of non est factum.  Translated literally from the Latin as "it is not my deed", it’s available as a defense where a person has been induced to sign something in circumstances where the contents of what was signed differ fundamentally from what the person was led to believe.  Where a plea is upheld, the court can set aside the contract (void ab initio).  Special circumstances must exist for the defense to succeed: it does not cover a claim where someone either misunderstood or failed to read the terms and conditions.

An octuple of Lindsay Lohan signatures on Lohanic merchandise. 

It’s novel in that it differs from other aspects of contract law such as the provisions which permit judges to strike-out particular clauses or even entire contracts if their enforcement is held to be “unconscionable”.  Non est factum is available even where terms and conditions can be reasonable such as the sale of a property for fair value; it hinges instead on the state of mind of the signee and the circumstances under which a signature was induced.  Typically, courts are most sympathetic to “innocent victims”, those who through no fault of their own (those illiterate, deaf, blind or suffering some other relevant incapacity) could not understand the document they were signing and relied upon another for advice.  Such is the reverence in contract law for the sanctity of the signature, a heavy evidential onus of proof is laid upon a claimant for non est factum to succeed; it’s a rare and exceptional defense.

The signature dish

Noted chefs and great restaurants often have signature dishes, not necessarily unique to them but something with which they’re famously associated.  Countries and regions also have signature dishes, sometimes advertised and promoted and sometimes just a link which develops over time.  There can even be disputes if the origin of something is thought a source of pride; there are factions in both Australia and New Zealand which lay claim to the pavlova. 

Minnesota Hotdish.

Despite the name, the concept of the Minnesota’s signature hotdish didn’t originate there and, with variations, is popular across the Upper Midwest region of the United States.  As a dish, such is the simplicity in preparation and adaptability in content that something recognizably close has probably been a feature of human cuisine for as long as the technical means of production has been available.  Anything of the hotdish type contains usually a starch, a meat, canned or frozen vegetables with canned soup as the binding agent; cooked in the one flat dish, it’s served heated.  The distinguishing characteristic of the classic Minnesota hotdish is the use of mushroom soup but beyond that, there’s much variation, inventiveness encouraged by the many hotdish completions in the region.  As well as the traditional beef base, tuna, turkey and chicken are used, pasta is often replaced by rice or potatoes and vegetarian versions have appeared.  The critical aspect seems to be the texture, while a Minnesota hotdish won’t entirely maintain the shape when sliced, it should have sufficient integrity for the potatoes or breadcrumbs to stay atop and not sink into the mix.

Hubert Humphrey, Cardinal Terence Cooke (1921–1983; Archbishop of New York 1968-1983) President Lyndon Johnson (LBJ, 1908–1973; US president 1963-1969) & Richard Nixon, twenty-third Alfred E Smith dinner, New York, 16 October 1968.  Cardinal Cooke was a less controversial figure than his predecessor (Cardinal Francis Spellman (1889–1967; prelate of the US Catholic Church & Archbishop of New York 1939-1967)).

Hubert Horatio Humphrey (1911–1978) served as a senator for Minnesota (1949-1964 & 1971-1978) and as US vice president (1965-1969).  He was the Democrat Party’s nominee for president in 1968, his candidature something of a rush-job after LBJ's abrupt decision not to seek re-election.  As part of the 1968 campaign, his wife’s Minnesota hotdish recipe was published, unusual today in that it didn’t include the potato gems which usually now sit atop the concoction.  Mrs Humphrey’s culinary campaign contribution wasn’t decisive, her husband, although running Republican Richard Nixon (1913-1994; US president 1969-1974) close in the popular vote (Nixon (31,783,783 votes; 43.4%), Humphrey (31,271,839; 42.7%)), lost the electoral college (Nixon, 32 states & 301 votes, Humphrey 13 states & 191 votes).

Mrs Humphrey’s Ingredients

4 tablespoons shortening
2 green bell peppers, sliced
1 medium onion, chopped
1 lb (500 g) ground beef
1½ half teaspoons salt
¼ teaspoon pepper
2 eggs
2 cups whole kernel corn
4 medium tomatoes, sliced
½ cup dry bread crumbs
Butter

Mrs Humphrey’s Instructions

(1) Put shortening in skillet; lightly fry green peppers, onion and ground beef for 3 minutes or until partially done. Salt and pepper. Remove from heat; stir in eggs and mix well.

(2) Place 1 cup corn in casserole. Top with layer of meat mixture and layer of sliced tomatoes.

(3) Repeat until corn, meat mixture and tomatoes are used.

(4) Cover casserole with crumbs. Dot with bits of butter.

(5) Bake at 375º F (190º C) for 1 hour or until heated thoroughly.

It can be finished in a grill to add something to the cheese.  Serve with a side salad and rolls.

Hitler's signature

Becoming tremulous: Hitler’s signature: 1933-1945.

Between 1943-1945, Adolf Hitler's (1889-1945; Führer (leader) and German head of government 1933-1945 & head of state 1934-1945) handwriting suffered and, towards the end, it took some effort even to etch his name, a process which happened in conjunction with a physical decline noted in many contemporary accounts.  The reason for this deterioration has been discussed by doctors, historians and popular authors, most recently in 2015 by Norman Ohler (b 1970) in Der totale Rausch: Drogen im Dritten Reich (The Total Rush: Drugs in the Third Reich), published in English in 2017 as Blitzed: Drugs in Nazi Germany (Penguin, ISBN: 9780141983165).  Blitzed is a study of the use of methamphetamine stimulants in German society, the military and Hitler himself during the Nazi years with a focus especially on the relationship between the Führer and his personal physician, Dr Theodor Morell (1886–1948) who prescribed and administered a variety of drugs and vitamins between 1936-1945.  It’s the use of opioids and psychoactive drugs that is of most interest.

A best seller, Ohler wrote a lively work in a jaunty style which made his book readable but did attract criticism from the academic and professional historians never happy with journalistic trespassing on their carefully trimmed turf.  While there’s always sensitivity to authors injecting elements of humour and pop-culture references into anything about Hitler and the Third Reich, these essentially stylistic objections matter less than the substantive concerns about presenting as proven fact inferences drawn from incomplete or inconclusive sources.  That critique of scholarship should be noted but Blitzed needs to be read as just another text interpreting the documents of the era and in that, if read in conjunction with other accounts of the time, Ohler’s thesis is in places compelling while sometimes contradicted by multiple other sources.  The argument that the drugs had no effect Hitler’s decline and increasingly erratic behavior were due to stress and the onset of Parkinson’s disease is as dogmatic a position as many accuse Ohler of taking.  There are interesting aspects in the accounts from 1943-1945: the unexpected way Hitler’s physical tremors briefly vanished in the aftermath of the explosion during the assassination attempt in July 1944 and the various clandestine analysis of Morell’s preparations, some of which revealed a strong opioid and some harmless concoctions with barely a pharmacological effect.  While clearly not a conventional work of history, Blitzed seems a valuable contribution.

Patient & doctor: Hitler and Dr Morell.

The fault in Blitzed is probably that habitual journalistic tendency to exaggeration.  That stimulants were widely available and demonstratively popular in Germany doesn’t mean the entire workforce, every hausfrau and all servicemen in the Wehrmacht were habitual or even occasional users of amphetamines although, given the documentary evidence and the observational accounts of behavior, the case for Hitler’s addictions (or at least dependence) is stronger.  Critics felt also compelled to run the usual objection to anything which could be constructed as some sort of exculpatory argument; the idea that being stupefied by psychoactive drugs could somehow absolve individual or collective guilt.  Among those who lived the Nazi experience, long has been established the guilt to one degree or another of the many and the innocence of a few.  That said, there seems little doubt the rapidity of the Wehrmacht's advances in 1939-1941 were at least partially attributable to the soldiers being supplied amphetamines which enabled a heightened level of alertness and performance for sometimes thirty hours without need for sleep.  It was a most effective force multiplier.  Other factors, notably (1) the revolutionary approach to deploying tanks as armored spearheads, (2) the used of dive-bombers, (3) the ineptness of the Allied response and (4) luck were more significance but the speed did make a contribution.