Rectilinear & Curvilinear

Rectilinear (pronounced rek-tl-in-ee-er)

(1) Forming or formed by straight lines.

(2) In geometry, as rectilinear grid, a tessellation by rectangles or rectangular cuboids (also known as rectangular parallelepipeds) that are not, in general, all congruent to each other.

(3) Of, pertaining to or characterized by straight lines.

(4) In, moving in, or characterized by a movement in a straight line or lines.

(5) In architecture, as the rectilinear style, the third historical division of English Gothic architecture.

1650–1660: From the post-Classical Latin, either from rectilīneāris or from rectilīneus (the source also of rectiline) + -ar, in either case the ultimate sources being rectus (straight) + līnea (line).  Rectus was from the primitive Indo-European root reg- (move in a straight line) with derivatives meaning "to direct in a straight line".  The suffix -ar is from the Latin from -ālis with dissimilation of “l” to “r” after roots containing an “l” thus āris and used to form adjectives (usually from a noun) to convey the sense of a relationship or “of; pertaining to”.  The English adjectival suffix –ar (of, near, or pertaining to) is widely appended, usually to nouns and is not restricted to those of Latin origin (the synonymous forms including -al, -an, -ary, -ese, -ic, -id, -ish, -like, -oid, -ory, -ous & -y).  Rectilinear came to be used in the sense of “a figure bounded by straight lines" by 1728, an evolution of the earlier meaning “straight lined”.  Rectilinear & rectilineal are adjectives, rectilinearity is a noun.

Curvilinear (pronounced kur-vuh-lin-ee-er)

(1) Consisting of or bounded by curved lines.

(2) Forming or moving in a curved line.

(3) Formed or characterized by curved lines.

(4) Of lines, having bends; curved.

(4) In mathematics, a set of coordinates determined by or determining a system of three orthogonal surfaces

1690s: From the Latin, derived from curvi (a combined form of the Latin curvus (crooked, bent, curved) + līneāris, from līnea (line).  The construct of līneāris was līnea (line) + -āris (the adjectival suffix).  The Latin curvus was ultimately from the primitive Indo-European sker & ker (to bend, curve, turn) + -wós (before it became associated with perfect stems, the suffixes -wós- & -us- had a more general function, forming athematic verb participles with the meaning "having x-en").  The earlier form was curvilineal, dating from the 1650s.  Curvilinear is an adjective, curvilinearity a noun and curvilinearly an adverb.

A juxtaposition of curvilinearity and rectilinearity: Lindsay Lohan, Vanity Fair shoot, October 2010.

In engineering, as in nature, matters of rectilinearity and curvilinearity tend to be products variously of inheritance, circumstance, economics or necessity.  In design however, sometimes fashion is allowed (indeed sometimes encouraged) to prevail over function and in automotive styling, the rectilinear (known in its most extreme form as knife-edge or razor-edge design) was a motif which came and went.  In the early days when things were truly little more than starkly functional, straight lines were dominant but the industry also inherited many of the traditions of the architecture of the horse-drawn carriage and embellishments could be quite curvaceous.  Line and curve co-existed in the inter-war years and as interest grew in streamlining to improve aerodynamics, the curves actually assumed a functional purpose.  At the same time, severity of line became itself a defined style, associated with formality and wealth, structurally because the straight lines tended to exaggerate size so the bigger cars appeared larger still and perhaps psychologically because they conveyed a message of casual disregard for something like streamlining, relying instead on power.  The big, bustle-backed limousines of the pre-war years were the exemplars.

Rolls-Royce Phantom IV (1950-1956 (left)), Triumph 1800-2000 Renown (1946-1954 (centre)) & Triumph Mayflower (1949-1953 (right)).

In the post war-years, in Europe and US, designers were attracted to the new.  In Europe that meant the avant-garde while across the Atlantic it could mean anything from restrained formalism to macropterous absurdity.  In England however, there was still a hankering for the familiar and among the coachbuilders (and Rolls-Royce which had begun building its own “standard” bodies) it was “business as usual” and, barely updated, the razor-edged lines returned.  Remarkably, as a niche, the style would be produced in tiny numbers until the 1990s even as modernity overtook the land.  So clearly, on a big scale it worked for the small, exclusive market at which it was targeted, a rolling denotation of wealth and power and this was what attracted others to apply the rectilinear lines on a smaller scale, at a lower price.  The leading proponents were Standard-Triumph which in 1946 released their middle-class 1800 as a kind of shrunken (though no less angular) Rolls-Royce or Bentley.  Generally, it was judged an aesthetic success although it quickly became dated and before long, the company was emulating American cars, their shrunken versions of those rather less pleasing.  The 1800 however maintained sufficient popularity to remain in production for eight years and that encouraged the idea the motif might translate well to something even smaller.  Hence in 1949, the Triumph Mayflower, small, stubby and wholly unsuited to a style which worked only at scale; the only thing more absurd than its existence was that the company designed it with the US market in mind.  The advertising agency suggested advertising it as “the watch charm Rolls-Royce” but whether that was vetoed by threats from Rolls-Royce or watch charm makers isn’t recorded.  A failure in every market in which it was offered (conspicuously so in the US), it was replaced by an anonymous-looking blob which might have designed by someone French in an unimaginative moment or an Italian on a bad day.

1967 Cadillac Eldorado (left), 1971 Fiat 130 Coupé (centre) and 1983 Volvo 760 GLE (right).

Until the oil shocks of the 1970s forced just about everyone to take aerodynamics seriously, the rectilineal would come and go as a fashion trend.  Cadillac’s 1967 Eldorado was an outstanding example and has aged better even than its curvier companion, the Oldsmobile Toroando of a year earlier but probably the high point of the modern razor-edge was Pininfarina’s Fiat 130 Coupé, its dimensions a stylistic sweet-spot which proved as suited to the saloon and shooting brake the designer world later exhibit; regrettably, neither reached production and the coupé proved a commercial failure, albeit one much admired.  That wasn’t something often said of one of Europe’s less successful straight-edged ventures, the 1982 Volvo 700 series.  Looking something like an earnest but uninspired student at a technical college might have submitted for assessment, Volvo at the time claimed it would remain timeless over the years to come while the rounded shapes around it soon became dated.  In that they were certainly wrong, the competition becoming more curvilinear still and soon Volvos nip-and-tuck specialists were finding ways to smooth the corners, not an easy task given the shape the patient was in and something really not possible until the re-skinned 900 was released in 1990.  The 700 had, by Volvo’s standards, a short life but it’s remembered for a bon mot from another designer who mused that it “…might be a good-looking car when they take it out of the packing-case”.

1953 Jaguar C-Type (XK120-C) continuation (left), 1957 Jaguar XKSS (centre) & 1961 Jaguar E-Type (XK-E) (1961).

Curves can be mere styling devices and in the 1960s General Motors (GM) actually created a motif they called cokebottle, summoning the idea of a Coca-Cola bottle on its side, itself evocative of the female form supine.  Plans to trademark the word were abandoned when the lawyers assured everyone using a lowercase “c” and claiming it to be a portmanteau word would fool neither the Coca-Cola company nor the judge.  Sometimes though, the curves were functional, Jaguar in 1950 shaping the aluminum skin on the XK120-C (C-Type) simply to be as low and aerodynamic as possible, the curves bulging only where necessary to provide coverage for the wheels and tyres.  On the subsequent D-Type (and the road-going derivative the XKSS), the impression was that the curves had become exaggerated, bulging more sensually still.  It’s not entirely an optical illusion but the shape is wholly functional, the designers actually lowering the centre, a revised mounting of a now dry-sumped engine permitting a lower bonnet (hood) line and thus a smaller frontal area.  The wheels and tyres remained much the same height so the curvature of the skin enveloping them is so much more obvious on a body otherwise lower.  The remarkably small frontal area did the job at Le Mans; the D-Type nearly 20 mph (32 km/h) faster than Ferrari's far more powerful 375.  By the time the E-Type was released in 1961, it could actually have been done with a little less curvature but we should all be grateful it looks as it does.

1960s original (left), 2022 modern (centre) & 2022 retro (right).

Objects like refrigerators offer designers a little more scope given that a low drag coefficient hardly matters although the modern, rectilinear versions presumably optimize space efficiency, offering the highest internal volume relative to external dimensions.  That said, there’s clearly still some demand for fridges which emulate the rounded style most associated with the 1950s and 1960s, several manufacturers with a retro line and they’re available in the pastel shades of the era.

Neon

Neon (pronounced nee-on)

In chemistry, a rare, colorless, odorless gaseous element; an inert gas (the second in the noble group) occurring in trace amounts in the atmosphere.  It glows reddish orange when electricity passes through it, as in a tube in an electric neon light, hence the industrial use in illuminated signs & lights although it’s used also in refrigeration because of the helpfully low melting & boiling points.

(2) A neon lamp, tube or device, in the singular or collectively; made of or formed by a neon lamp or lamps.

(3) A sign or advertising display formed from (or emulating) neon lamps.

(4) Of, relating to, or characteristic of an urban area brightly lit during hours of darkness and often associated with popular forms of entertainment.

(5) As in the phrase “in neon”, or “in neon lights”, adding emphasis to something (sometimes used derisively).

(6) Any of a range of bright, lurid colors, used particularly in fashion (lipsticks, nail polish etc) and as hair color products.

(7) As neon tetra (Paracheirodon innesi), a freshwater fish of the characin family (family Characidae) of order Characiformes, native to the Amazon basin in South America.  Because of its vivid coloring and robustness, the neon tetra is one of the most popular tropical fish in home aquariums.

1898: From the Ancient Greek νέον (néon), neuter of νέος (néos) (new; young), from the earlier νέϝος (néwos), from the Proto-Hellenic newos, from the primitive Indo-European néwos.  From the same source, English (and other languages gained the prefix –neo which was often used to form clade or taxonomic names indicating more recent branching than a morphologically or otherwise similar group.  The prefix neo- was from the Ancient Greek prefix νεο- (neo-), from νέος (néos) (new, young).  In organic chemistry it (1) had the specific technical meaning “having a structure, similar to that of neopentane, in which each hydrogen atom of a methyl group has been replaced by an alkyl group” and (2) a newly-discovered or synthesized variant of an existing compound.  The synonyms (in the sense of something new) were ceno- & nov-, the less used antonym paleo-.  Many words have been prefixed with neo- and not exclusively to indicate something wholly novel but increasingly to describe a revival or new variation of something including (1) in architecture: neo-classical, neo-gothic etc, (2) in economics: neo-liberal, neo-Keynesian etc, (3) in politics: neo-Nazi, neo-conservative, neo-fascist etc and (4) in religion: neo-evangelicalism, neo-Hasidism etc.  In chemistry, the meaning is quite specific but in general use the synonyms include blazing, brilliant, glowing, lambent, luminous, radiant, shining, vivid, flashing, glitzy, glossy, razzle-dazzle, effulgent & gleaming.  Neon is a noun & adjective; the noun plural is neons.

Sohio “Neon Patrol” in action, Cleveland, Ohio, July 1938.  Technicians from the Neon Patrol would travel between the company’s retail outlets, servicing the neon signage and effecting repairs when required.  The truck is an International D-15 with a special body.  The D Series (1937-1939) was a range of light, medium & heavy-duty trucks, easily distinguished from the more rectilinear C Series (1934-1936) by the curvilinear lines and the two-piece V-shaped windshield.  The line was replaced by the K (1940-1946) & KB Series (1947-1950).

The Standard Oil Company (Ohio) was a US petroleum company which operated between 1870-1987 and Sohio was one of a number of separate entities created in 1911 after the Standard Oil corporate trust (1882-1911) was broken up.  Standard Oil and British Petroleum (BP) in the 1960s entered into an intriguing (and tax-friendly) arrangement whereby BP gradually would increase its stake in Standard Oil, culminating eventually in acquisition.  Sohio as a corporate identity ceased operations in 1987 but BP continued to sell gas (petrol) under the brand until 1991, the name formally retired when the branding on the last Sohio gas station was replaced with BP signage.

Neon

Symbol: Ne.
Atomic number: 10.
Atomic weight: 20.1797.
Valency: 0.
Density: 0.899 90 kg/m³ / 0.9002 gm/liter at 0°C & 760 mm pressure.
Melting point: –248.59°C.
Boiling point: –246.08°C.

Neon nail-polish in 5-pack by Casey's Toys (part-number 52123) @ Aus$9.99.

Although in the United States it’s possible for citizens (in some cases children) lawfully to possess military-grade firearms and some truly impressive ordinance, in other fields the government is punctilious in providing people protection.  In 2012, Douglas Schoon (b 1954), Creative Nail Design (CND)’s chief scientific advisor, explained that in the US, the manufacture of neon nail-polish was unlawful, although, in what seemed a quirk of the law, the products remain lawful to wear.  However, that apparent anomaly isn’t actually strange or unique to neon nail-polish and reflects a regulatory environment where the need is to certify the safety of both the components and the processes used in the manufacturing process.  There are no concerns about the safety of the finished product, the skin and nails anyway a most effective barrier and the nature and volume of fumes breathed in by consumers “doing their nails” would substantively be identical to that of other nail-polishes.

Coffin-shaped nails in neon-green.  These are actually "press-on nails".

Neon polishes are prohibited simply because the colorants have never been officially registered with the US Food & Drug Administration (FDA).  Mr Schoon explained that “…what determines whether a color is neon is the chemical composition, just as it is with blues and greens”, adding that that any manufacturer could submit neon shades to the FDA, but it’s a costly and time-consuming process which is why many of the lurid shades available in the US, technically, are not neons.  Registration is only the first step in securing FDA approval and few small-scale manufacturers have the resources to go through a process from which others would gain equal benefit.  Imported neon polishes appear on many shelves but it’s not known if unlawful, small-scale manufacturing is being undertaken somewhere in the US.

Lindsay Lohan (b 1986, left) in neon outfits and singer-songwriter Billie Eilish (b 2001, right) with neon highlights.  Ms Eilish also went blonde, the result thought most pleasing.

As an adjective used of colors, neon refers to the quality of brightness rather than the red-orange colour which is the particular property of neon gas under electrical stimulation.  Thus, a “neon color” (or simply “neon”) is anything bright, lurid and used in clothing, accessories & enhancements (lipsticks, nail polish etc) or hair color products.

"Neon" advertising displays, Piccadilly Square, London, 1967.

Neon was discovered in 1898 by British chemists Sir William Ramsay (1852–1916) and Morris Travers (1872–1961) while working in their London laboratory during a series of experiments which also uncovered krypton & xenon, the other two residual rare inert elements remaining in dry air after nitrogen, oxygen, argon and carbon dioxide are removed.  In normal conditions a colorless, odorless & inert monatomic gas, it has about two-thirds the density of air and is noted for its emission in the spectrum of bright red when exposed to electrical current.  Although one of the known universe’s most common elements (fifth behind hydrogen, helium, oxygen and carbon), it’s rare on Earth, existing only in trace amounts in the atmosphere, attributable to it being highly volatile and thus never forming compounds which assume any solidity.

It needs thus to be extracted from air by an industrial process so is relatively expensive, its industrial uses limited to some specialized applications in refrigeration (by virtue of its low melting & boiling points) and the famous “neon lights” most associated with advertising and signage, the first of which was released in 1913, the term “neon sign” dating from 1927.  The distinctive bright red (tending to orange) light distinguished the first neon signs (created with curved neon-tubes) and in the narrow technical sense these are the only true “neon-lights” because tubes which generate other colors are made using either other noble gases or are instances of fluorescent lighting.  In hidden use, neon is also a component of various electrical devices including vacuum & wave tubes, current indicators and lightning arresters.

Tokyo after dark: less pink, more blue.

For decades, pink was the dominant color in the night-time Tokyo streetscape but in the twenty-first century observers began noting a shift to something darker.  The change is attributed not to the nation’s post 1989 slump in economic growth (the so-called “lost decade” of the 1990s apparently never having ended) but the development in 1993 by Japanese-American engineer Shuji Nakamura (b 1954) of a high-efficiency blue LED (light emitting diode) using gallium nitride (GaN) as the semiconductor material.  While green and red LEDs had for decades been in use, blue had proved elusive because the industry lacked a material suitable (and sufficiently cheap) to use at scale.  Nakamura san’s work built on earlier research by Japanese physicists Isamu Akasaki (1929–2021) and Japanese physicist Hiroshi Amano (b 1960) and what the three did was make possible both blue and white LEDs, the latter enabled by combining the blue with phosphors.  In 2014, the three were awarded the 2014 Nobel Prize in Physics.

1970 Plymouth Hemi 'Cuda in Limelight (left) and 2023 Dodge Challenger SRT Hellcat Redeye Jailbreak in Sublime (right). 

Lurid neon hues began to fade from the roads after being banished from the automotive color charts in the mid 1970s and while it can be debated if that was an aesthetic loss, it certainly made the option lists less linguistically interesting.  Like other manufacturers, Chrysler had some history in the coining of fanciful names for colors dating from the psychedelic era of the late 1960s when the choices included Plum Crazy, In-Violet, Tor Red, Limelight, Sub Lime, Sassy Grass, Panther Pink, Moulin Rouge, Top Banana, Lemon Twist & Citron Yella.  Although it may be an industry myth, the story told is that Plum Crazy & In-Violet (lurid shades of purple) were late additions because the killjoy board refused to sign-off on Statutory Grape.  Plymouth called their lime green Limelight while Dodge used Sub Lime.  That the colors vanished during the 1970s was not because of changing tastes but in response to environmental & public health legislation which banned the use of lead in automotive paints; without the additive, production of the bright colours was prohibitively expensive.  Advances in chemistry meant that by the twenty-first century brightness could be achieved without the addition of lead so Dodge revived psychedelia for a new generation although Sub Lime became Sublime.  There was still a price to be paid however, Sublime, Red Octane, Sinamon Stick and Go Mango all costing an additional US$395 while the less vivid shades listed at US$95.  The resurrected "neon look" proved popular although only within the high-performance niche, most of the market preferring more "dignified" tones such as black, white, silver and many variations of gray although there's still the odd malcontent who orders blue or red.

2015 Dodge Challenger SRT in Sublime (code FB).  Literalists should note this is NOT what Greta Thunberg (b 2003) meant when she spoke of "green vehicles".

There was of course once a time when the term “green vehicle” had a simple, unambiguous meaning but were a driver to contest a parking ticket, the outcome might depend on how a court would apply the “Vagliano rule”, established by the House of Lords in Bank of England v Vagliano Bros (1891) AC 107.  The Vagliano rule is a principle of statutory interpretation and holds that when interpreting a statute, courts should start by considering the natural meaning of the words in the statute itself, without referring to previous case law or historical background, unless the language is ambiguous.  The rule is of such significance because it prioritizes the literal and ordinary meaning of words over any interpretation which could be derived if other factors are allowed to intrude.

In his judgment, Lord Herschell (Farrer Herschell, 1837–1899; Lord High Chancellor of Great Britain 1886 & 1892-1895) wrote: “I think the proper course is, in the first instance, to examine the language of the statute and to ask what is its natural meaning, uninfluenced by any considerations derived from the previous state of the law, and not to start with inquiring how the law previously stood, and then, having ascertained that, to see whether the statute will bear an interpretation which is in accordance with it. If the statute is clear, its provisions must prevail, whatever the previous law may have been. If the statute is ambiguous, then, and only then, may the history of the law be referred to.”  Whether in the 2020s a judge would be persuaded “Green Vehicle” should for this purpose be read-down to permit gas-guzzling V8s (simply on the basis of being painted a certain color), to occupy parking spots allocated exclusively to the machines of which Ms Thunberg would approve may be doubtful but any driver will always be able to find a lawyer willing to run the case.