Perpendicular

Perpendicular (pronounced pur-puhn-dik-yuh-ler)

(1) Vertical; straight up and down; upright; normal at right angles to a horizontal plane.

(2) In geometry, meeting a given line or surface at right angles.

(3) Maintaining a standing or upright position; standing up; exactly upright; extending in a straight line toward the centre of the earth, etc.

(4) In architecture, noting or pertaining to the last style of English Gothic, prevailing from the late fourteenth to the early sixteenth centuries and characterized by by stiff, rectilinear lines and the use of predominantly vertical tracery, an overall linear, shallow effect, depressed or four-centre arch, fan-tracery vaulting, panelled walls and fine intricate stonework (should be used with an initial capital letter so it’s not confused with being a purely geometric reference).

(5) In rock-climbing, a sharply pitched or precipitously steep mountain face.

(6) Moral virtue or uprightness; rectitude (largely obsolete).

(7) In Admiralty jargon, either of two lines perpendicular to the keel line, base line, or designed water line of a vessel.

(8) In surveying, a device such as a plumb line that is used in making or marking a perpendicular line.

(9) In historic slang, a meal taken while standing at the bar of a tavern (obsolete).

1350–1400: From the Middle French perpendiculaire, from the Old French perpendiculer, from the Latin perpendiculāris (vertical, as a plumb line), the construct being perpendicul(um) (plumb line), from pendēre (to weigh hang) and perpendere (carefully to balance (the construct of which was per- (thoroughly) + pendēre (to hang, cause to hang; to weigh)) from the primitive Indo-European root spen & pen (to draw, stretch, spin) + āris.  The suffix -aris was a form of -ālis with dissimilation of -l- to -r- after roots containing an l (the alternative forms were -ālis, -ēlis, -īlis & -ūlis); it was used to form adjectives, usually from noun, indicating a relationship or a "pertaining to”.  The French borrowing replaced the Middle English perpendiculer(e) and is the source of the modern pendant.  The noun from existed from the 1570s (the earlier noun was the circa 1400 perpendicle) and in astronomy, navigation and related matters, it was in the late fifteenth century the sense of a line "lying at right angles to the horizon" developed from an earlier adverb referring to "at right angles to the horizon.

The noun perpensity (consideration, a pondering, careful attention) appears first to have been used in the early eighteenth century, the construct being the Latin perpens- (past-participle stem of perpendere (carefully to balance) and has since the late nineteenth century been listed either as archaic or obsolete.  Perpendicular is a noun and adjective, perpendicularness & perpendicularity are nouns and perpendicularly is an adverb; the noun plural is perpendiculars.  Although perpendicular describes what nominally is an absolute value, most dictionaries acknowledge the comparative more as perpendicular & the superlative as most perpendicular, reflecting the use of the word to describe also the “quality of that which tends towards”, hence the existence in geometry, mathematics, architecture & engineering of the presumably helpful adjective quasiperpendicular to refer to the mysterious “partially perpendicular”.

In audio engineering, a perpendicular recording is the technique of creating magnetic data storage using vertical as opposed to longitudinal magnetization.  The synonym used in a technical context is orthogonal (independent of or irrelevant to each other).  To most, the idea of the perpendicular is simple but it’s been borrowed to describe some complex concepts such as the perpendicular universe (though these perhaps by definition seem usually to be referred to in the plural as perpendicular universes) which exists to distinguish it from a parallel universe (which must in some way be different).  The perpendicular universe is thus one of the competing notions (some insist these are legitimate theories) of multiple universes which are in some way parallel (as opposed to sequential or circular) though not of necessity perpendicular.  Seems clear enough.

The Perpendicular Pronoun:  The first-person singular pronoun "I"

There is a general rule defining when to use “I” or “me” in a sentence and that is the first person singular pronoun is “I” when it’s a subject and “me” when it’s an object (the subject is the person or thing doing something, and the object is having something done to it and the often quoted example to illustrate the difference is the sentence “I love you”.  “I” is the subject of the sentence. “You” is the object of the sentence (also the object of one's affection).

Lindsay Lohan and her sister Aliana at the Melbourne Cup, 2019.

In most cases it’s easier to deconstruct the sentence than think about the rule.  To work if one should say (1) “Lindsay and I are going to the Melbourne Cup” or (2) “Lindsay and me are going to the Melbourne Cup”, deconstruction confirms (1) is correct because “I am going to the Melbourne Cup” works and “Me is going to The Melbourne Cup” does not.  That’s fine but because “me” is often wrongly used, something of a perception has evolved to suggest it must always be wrong and “I” must always be correct. However, everything depends on the sentence.  It’s correct to say “Lindsay and I both picked the winning horse” but it’s also right to say “A selfie of the winning horse with Lindsay and me”, something which can be checked by redacting either “Lindsay and” or “and me”.

Lindsay Lohan in Falling for Christmas (Netflix, 2022)

Modern English use has anyway actually banished the perpendicular pronoun from places where once it was a marker of the educated.  To say “It is I” remains supported by historic grammatical correctness but sounds now so strange (because the common form is “It’s me”) that many would it’s wrong.  Pedants fret over things like this but the world has moved on and if in answer to the question “Is that you Ali” the response came “This is she”, the antiquated correctness might discombobulate one while “It’s me” would not.

Athwart

Athwart (pronounced uh-thwawrt)

(1) From side to side; crosswise, transversely.

(2) In admiralty use, at right angles to the fore-and-aft line; across.

(3) Perversely; awry; wrongly.

1425-1475: From the Late Middle English athwert & athirt and a proclitic form of preposition; the construct was a- (in the sense of "in the direction of, toward")  + thwart.  The a prefix was from the Old English an (on) which in Middle English meant “up, out, away”, both derived from the Proto-Germanic uz (out), from the primitive Indo-European uds (up, out); cognate with the Old Saxon ā which endures in Modern German as the prefix er.  Thwart was from the Middle English adverb & adjective thwert, (crosswise; (cooking) across the grain, transverse; counter, opposing; contrary, obstinate, stubborn), a borrowing from Old Norse þvert (across, transverse), originally the neuter form of þverr (transverse, across), from the Proto-Germanic þwerhaz, altered or influenced by þweraną (to turn) and þerh, from the primitive Indo-European twork & twerk (to twist).  Cognates include the Old English þweorh (transverse, perverse, angry, cross), the Danish tvær, the Gothic þwaírs (angry), the West Frisian dwers (beyond, across, to the other side of), the Dutch dwars (cross-grained, contrary), the Low German dwars (cross-grained, contrary) and the German quer (crosswise; cross).  The modern English queer is related.  Although still used by poets good and bad, the word is probably otherwise obsolete for all purposes except historic admiralty documents.  Athwart is a noun & adverb, athwartship is an adjective & adverb and athwartships & athwartwise are adverb; the noun plural is athwarts.  Forms like athwartly are definitely non standard.

In nautical design, the term “athwart” is used to describe a direction or orientation that is perpendicular to the centreline of a ship or boat (ie that which runs across the vessel from side to side (port-to-starboard) at right angles to the fore-and-aft line.  In shipbuilding this can apply to various components and actions on a ship, such as beams, futtocks, bulkheads, or even the positioning of objects; as a general principle something can be said to be “athwart” if it sits perpendicular to the centreline but the term is most often applied to objects which span or crosses the vessel’s entire width.  In naval architecture specifically, athwart was used as a noun to refer to the cross-members which sat beneath the deck-mounted gun-turrets on warships.  Although they had long been a part of the supporting structures, the term “athwart” seems first to have been used on the blueprints of HMS Dreadnought, launched in 1906 and a design thought so revolutionary it lent its name to the class of the biggest battleships, previous such vessels immediately re-classified as “pre-dreadnoughts” and, when even bigger ships were launched, they were dubbed “super-dreadnoughts”.

Lindsay Lohan with former special friend Samantha Roinson, athwart, TV Guide's sixth annual Emmy after party, The Kress, September 2008, Hollywood, California.

Samuel Taylor Coleridge (1772-1834), Kubla Khan (1798)

In Xanadu did Kubla Khan
A stately pleasure-dome decree:
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea.
So twice five miles of fertile ground
With walls and towers were girdled round:
And here were gardens bright with sinuous rills
Where blossomed many an incense-bearing tree;
And here were forests ancient as the hills,
Enfolding sunny spots of greenery.
But oh! that deep romantic chasm which slanted
Down the green hill athwart a cedarn cover!
A savage place! as holy and enchanted
As e'er beneath a waning moon was haunted
By woman wailing for her demon-lover!
And from this chasm, with ceaseless turmoil seething,
As if this earth in fast thick pants were breathing,
A mighty fountain momently was forced;
Amid whose swift half-intermitted burst
Huge fragments vaulted like rebounding hail,
Or chaffy grain beneath the thresher's flail:
And 'mid these dancing rocks at once and ever
It flung up momently the sacred river.
Five miles meandering with a mazy motion
Through wood and dale the sacred river ran,
Then reached the caverns measureless to man,
And sank in tumult to a lifeless ocean:
And 'mid this tumult Kubla heard from far
Ancestral voices prophesying war!
The shadow of the dome of pleasure
Floated midway on the waves:
Where was heard the mingled measure
From the fountain and the caves.
It was a miracle of rare device,
A sunny pleasure-dome with caves of ice!
A damsel with a dulcimer
In a vision once I saw:
It was an Abyssinian maid,
And on her dulcimer she played,
Singing of Mount Abora.
Could I revive within me
Her symphony and song,
To such a deep delight't would win me
That with music loud and long,
I would build that dome in air,
That sunny dome! those caves of ice!
And all who heard should see them there,
And all should cry, Beware! Beware!
His flashing eyes, his floating hair!
Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honey-dew hath fed,
And drunk the milk of Paradise.

Hilt

Hilt (pronounced hilt)

(1) The handle of a sword or dagger.

(2) The handle of any weapon or tool.

(3) To furnish with a hilt.

(4) As the idiom “to the hilt”, to the maximum extent or degree; completely; fully.

Pre 900:  From the Middle English, from the Old English hilt & hilte (handle of a sword or dagger); cognate with the Middle Dutch hilt & hilte, the Old Norse hjalt, the Old Saxon helta (oar handle) and the Old High German helza (handle of a sword).  Source was the Proto-Germanic helt, heltą, heltǭ, heltō & hiltijō, probably from the primitive Indo-European kel- (to strike, cut).  One form of the idiom which died out was “up to the hilts”, the plural having exactly the same meaning as the still familiar singular; first noted in the 1670s, it was extinct by the mid-eighteenth century except in Scotland and the border regions of northern England where it survived another hundred-odd years.  The vivid imagery summoned by the expression “to the hilt” is of a dagger stabbed into someone’s heart, the blade buried all the way to the hilt.  The phrase is used to suggest one’s total commitment to something although those training British commandoes in such things during World War II did caution that a blade buried in a victim "to the hilt" could be "difficult to get it out", such were "the contractions of the sinews".

Hilt is a European swordsmith’s technical name for the handle of a knife, dagger, sword, or bayonet; the once used terms haft and shaft have long been obsolete.  The hilt consists of a pommel, grip and guard.

Lindsay Lohan with saw-tooth edged dagger held at the hilt; from a Tyler Shields (b 1982) photo session, 2013.

The pommel is the large fitting at the top of the handle, originally developed to prevent the weapon slipping from the grasp but during the late medieval period, swordsmiths began to add weight so they were sufficiently heavy to be a counterweight to the blade.  This had the effect of shifting the point of balance closer to the hilt, the physics of this assisting swordsmanship.  The pommel could also be used as a blunt instrument with which to strike an opponent, something from the German school of swordsmanship known as the Mordhau (or Mordstreich or Mordschlag (literally "murder-stroke" or "murder-strike" or "murder-blow") method, a half-sword technique of holding the sword inverted, with both hands gripping the blade while striking one's opponent with the pommel or crossguard.  The technique essentially makes as sword function as a mace or hammer and in military training was envisaged for use in armoured combat although in the hands of a skilled exponent it could be deadly in close combat.  Some hilts were explicitly designed for this purpose.  The word pommel is from the Middle English pommel (ornamental knob or ball, decorative boss), from the Old French pom (hilt of a sword) & pommel (knob) and the Medieval Latin pumellum & pōmellum (little apple), probably via the Vulgar Latin pomellum (ball, knob), diminutive of the Late Latin pōmum (apple).  The use in weaponry came first, the sense of "front peak of a saddle" dating from the mid 1400s and in fifteenth and sixteenth century poetry it also sometimes meant "a woman's breasts".  The gymnast's pommel horse (vaulting horse) is so called by 1908, named for the removable handles, which resemble pommels of a saddle, the use in saddlery noted first in 1887.

Grips are still made almost always of wood or metal and once were usually wrapped with shagreen (untanned tough leather or shark skin) but this proved less durable in climates with high-humidity and in these regions, rubber was increasingly used from the mid-nineteenth century.  Whatever the material, it’s almost always both glued to the grip and wrapped with wire in a helix.  The guard sits between grip and blade.  The guard was originally a simple stop (a straight crossbar perpendicular to the blade (later called a quillon)) to prevent the hand slipping up the blade but later evolved into an armoured gauntlet to protect the wielder's entire hand from an opponent’s sword.  By the sixteenth century, guards became elaborate, now often decorative as well as functional, the innovation of this time being a single curved piece alongside the fingers (parallel with the blade and perpendicular to any cross-guards); it became known as the knuckle-bow.

Fishnet

Fishnet (pronounced fish-net)

(1) A net for catching fish.

(2) A fabric with an open mesh, resembling a fishnet.

(3) Being of an open-mesh weave.

(4) In fashion as a clipping of “fishnet stockings” & “fishnet tights”, usually in the form “fishnets”.

(5) In mathematics, geometry and mapping, as “fishnet grid”, a grid of equally-sized (usually square or rectangular) cells which can be overlaid onto another representation for various purposes.  

Pre 1000: from the Middle English, from the Old English fiscnett, the construct being fish + net.  Fish was from the Middle English fisch, from the Old English fisċ (fish), from the Proto-West Germanic fisk, from the Proto-Germanic fiskaz (fish).  It may be compared with the West Frisian fisk, the Dutch vis, the German Fisch, the Danish, Norwegian & Swedish fisk and the Icelandic fiskur, from the primitive Indo-European peysḱ- (fish) (the equivalent form in was iasc and in Latin piscis.  Net was from the Middle English nett, from the Old English net & nett, from the Proto-West Germanic nati, from the Proto-Germanic natją, from the primitive Indo-European ned- (to turn, twist, knot).  It was cognate with the West Frisian net, the Low German Nett, the Dutch net, the German Netz, the Danish net and the Swedish nät.  Fishnet is a noun & adjective; the noun plural is fishnets.

The most obvious “fishnet grid” is of course the fishnet, used by fishers to catch fist and one of the oldest technologies still in use with its essential design unchanged although much has changed in terms of materials, scale and techniques of use.  The same design (a grid structure with equal sized cells) is used in various field including (1) concreting where the steel reinforcing for slabs is used in this form, either in pre-made sections or assembled on-site.  (2) In agriculture, the grids are used as a support structure for climbing plants like beans which grow up the grid, gaining enhanced exposure to airflow and sunlight; ultimately, the arrangements also make harvesting easier and cheaper.  Made now with slender, strong, cheap and lightweight plastic strands which don’t absorb moisture, like the nets used to harvest fish, the agricultural mesh is produced in a variety of cell sizes, the choice dictated by the crop. (3) In architecture and interior decorating, grids are common design element, sometimes integrated into structural members and sometimes merely decorative.  (4) In fashion, the most famous fishnet grids are of course those used on stockings & tights where the most frequently seen patterns are diamonds or squares displayed with points perpendicular.  When used of other garments, the orientation of the cells can vary. (5) In industrial design, fishnet grids made of durable materials like steel or synthetic fibers are widely used, providing structures which can be lighter than those made with solid materials yet, in a seeming paradox, be stronger, at least in the direction of the stresses to which they’ll be exposed.  Such constructions are often used in support structures, fencing and other barriers.

North America with the lines of latitude & longitude as traditionally depicted in maps using a fishnet grid (left) and in a form which reflects the effects of the curvature of the earth.

In cartography, the most famous fishnet grid is that made up from the lines of latitude & longitude which, east & west, north & south, encircle the globe and have for centuries been used for navigation.  However, the familiar representation of the lines of latitude and longitude as a fishnet grid is illusory because the common, rectangular map of the world is just a two-dimensional rendering of a three dimensional sphere.  For most purposes, the flat map is ideal but when lines of latitude & longitude were added, so were distortions because the lines of longitude converge at the poles, becoming progressively closer as they move away from the equator.  Never parallel on the sphere which is planet Earth, on a map the lines are exactly parallel; a perfect fishnet grid.

The politics of the Mercator Map

The Mercator projection was developed in 1568 by Flemish geographer, cosmographer & cartographer Gerardus Mercator (1512–1594) as a navigation tool with spherical planet earth depicted on a flat rectangular grid with parallel lines of latitude and longitude.  Its functionality was such that in the west, it became the standard technique of projection for nautical navigation and the de facto standard for maps and charts.  For seafarers it was invaluable; all they needed do was follow the line on the chart and, barring accidents, they would arrive where intended.  However, the Mercator map is a most imprecise representation of the precise shapes and relative sizes of land masses because the projection distorts the size of objects as the latitude increases from the Equator to the poles, where scale becomes infinite.  That’s why land-masses such as Greenland and Antarctica appear much larger than they actually are, relative to equatorial areas such as central Africa.

The Mercator map (left), the distorting effect of the Mercator projection with the real size in the darker shade (centre) and the actual geography of Earth's land masses (right).

In the twentieth century, that distortion attracted criticism on the grounds the projection tended to increase the size of the land-masses of the European colonial powers while reducing those in the colonized south.  However, neither Gerardus Mercator nor other cartographers had social or political axes to grind; the geographical distortion was an unintended consequence of what was designed as a navigational device and it's anyway impossible accurately to depict the surface of a sphere as a two-dimensional rectangle or square (the so-called "orange-segment" renditions are dimensionally most accurate but harder to read).  The Mercator map is no different from the map of the London Underground; a thing perfect for navigation and certainly indicative but not to exact scale.  Modern atlases generally no longer use the Mercator map (except for historical or artistic illustrations) but they’re still published as wall-maps.

The Tube

The classic "map" of the London underground is an ideal navigational aid but, conceptual rather than being drawn to scale, applying a fishnet grid would be both pointless and without meaning.  Professional cartographers refer to such things as "diagrams" or "mud maps", the latter a colloquial term which began life in the military and was a reference to the improvised "maps" drawn in the soil by soldiers in the field.  While not precise, to scale or a detailed representation of an area, they were a simple visual aid to assist in navigation.

Fishnet fan Lindsay Lohan: Confessions of a Teenage Drama Queen (2004), (left), Elle Style Awards, London, February 2015 (centre) and Cannes Film Festival, May 2017 (right).  

There are both fishnet tights and fishnet stockings and unless worn in a manner to permit an observer to discern which, whether it’s one or another is often known only to the wearer, the distinction blurred further by manufacturers being sometimes inclined to be a bit loose with their labeling.  While both items of leg-wear, there are technical differences in the construction, coverage and style.  Tights should be made of a thicker, more opaque material which affords complete coverage from the waist to the toes.  Although a fashion item, the historic purpose of tights was to keep the legs warm in cold weather and they were a garment of some importance when there were dress codes which denied women the right to wear trousers.  Constructed almost always in one piece, tights have an elastic waistband which has the primary purpose of keeping them in place but there are some tights which technically are “shapewear”, the midsection an expanded, all-round elastic panel which has a mild compression effect on the areas around and immediately above the hips, rendering a more trim silhouette.  Except for a handful of high-priced products, tights use relatively thick materials like nylon or spandex (sold as lycra in some markets).  There are also composite materials now available which has meant the range of thicknesses, colors and patterns offered has been expanded and the finishes range from semi-sheer to opaque, making them suitable for casual and formal occasions while still providing protection from the cold.  The essential difference between tights and leggings is the later are shorter, stopping anywhere from the ankle to the upper calf (although some specialized sports leggings extend only to somewhere above the knee).

Classically, stockings were designed to cover only the legs between the upper-thigh and the toes.  Made typically from a sheer material, they are held in place by a device called a “garter belt” or “suspender belt” which sits around the hips, two (sometimes three) elastic “suspender slings” (a marvelous name) are attached to each side at the ends of which are metal clips into which a rubber or silicone disc is inserted through the stocking material, holding it permanently in place.  Usually sheer in a color spectrum from black to white (with a solid emphasis of “skin tone” although sensitivity to the implications of that term means it now less used), patterns are also available and among the most popular is the single, emulated “seam” running vertically up the back of the leg.  Until the mid twentieth century, stockings were made almost exclusively from silk are they remain available but the majority use some form of synthetic, either nylon or a nylon-mix and are thought to impart both a more delicate and refined look and are thus associated with formal attire.  The modern hybrid which has since the 1970s captured most of the stocking market is “pantyhose” (the construct being a portmanteau of the modified clippings of panties (panty) + hosiery (hose).  Pantyhose used the design of tights and the sheer material of stockings, the obvious advantage being the convenience of not needing the belt apparatus with its alluring but fiddly “suspender slings”.  Fishnet pantyhose are available.

Slant

Slant (pronounced slant or slahnt)

(1) A surface, structure, line etc at a slope or in an oblique direction.

(2) In (US) football, an offensive play in which the ball-carrier runs toward the line of scrimmage at an angle (known also as the “slant-in”, a pass pattern in which a receiver cuts diagonally across the middle of the field).

(3) In prosody, as “slant rhyme”, a synonym for the “half rhyme”, “near rhyme” & “quasi-rhyme” (a form of imperfect rhyme in which the final (coda) consonants of stressed syllables (and, in modern English poetry, any following syllables to the end of the words) are identical in sound, but the vowels of the stressed syllables are not.

(4) In typography, a synonym of slash ( / ⟩, particularly in its use to set off pronunciations from other text (not used in IT where the distinctions are between the forward-slash (/) and the back-slash (\) which nerds call respectively the slash and the slosh.

(5) In biology, a sloping surface in a culture medium.

(6) In hydro-carbon extraction, as “slant drilling”, a technique in which the drilling is undertaken at an oblique angle rather than the traditional vertical orientation.

(7) In extractive mining, as type of run in which a heading is driven diagonally between the dip and strike of a coal seam.

(8) In informal use, a glance or look.

(9) To veer or angle away from a given level or line, especially from a horizontal; slope (in to incline, to lean).

(10) Figuratively, to have or be influenced by a subjective point of view, bias, personal feeling or inclination etc (often as “slant towards”, “slanted view” etc); a mental leaning, bias, or distortion (“feminist slant”, “MAGA slant”, “liberal slant”, “business slant” et al).

(11) To cause to slope.

(12) Figuratively, to distort information by rendering it unfaithfully or incompletely, especially in order to reflect a particular viewpoint (more generously sometimes described as “spin” or “massaged”).  The concept is known also as “angle journalism” (the particular mood or vein in which something is written, edited, or published).  In Scots English, the meaning “to lie or exaggerate” captures the flavor.  When used to describe the composing, editing, or publishing of something to attract the interest of a specific sub-group (a “slanted” story), “slanted towards” is necessarily pejorative if used only to suggest something optimized to appeal to a certain market segment or demographic (ie it’s more like “aimed at” or “intended for”).

(13) In slang, as “slant eye” (a racial slur now listed as disparaging & offensive), a reference to people from the Far East (applied historically mostly to the Chinese & Japanese), based on the shape of the eyes.  The variants included “slit eye”, “slitty-eyed” & “slopehead”, all equally offensive and now proscribed.

(14) In painting (art) a pan with a sloped bottom used for holding paintbrushes; a depression on a palette with a sloping bottom for holding and mixing watercolors; a palette or similar container with slants or sloping depressions.

(15) In US regional slang, a sarcastic remark; shade, an indirect mocking insult (archaic).

(16) In US slang, an opportunity, particularly to go somewhere (now rare).

(17) In historic Australian colonial slang, a crime committed for the purpose of being apprehended and transported to a major settlement.

Circa 1480s: From the Middle English –slonte or -slonte, both aphetic (in phonetics, linguistics & prosody, “of, relating to, or formed by aphesis” (the loss of the initial unstressed vowel of a word)) variants of aslant, thought to be of Scandinavian origin.  The other influence was probably the earlier dialectical slent, from the Old Norse or another North Germanic source and cognate with the Old Norse slent, the Swedish slinta (to slip) and the Norwegian slenta (to fall on the side), from the Proto-Germanic slintaną (which, in turn, was probably in some way linked with aslant.  Slant & slanting are nouns, verbs & adjectives, slanted is a verb & adjective, slantish is an adjective, slantwise is an adjective & adverb and slantingly & slantly are adverbs; the noun plural is slants.  The pleasing adjective slantendicular is listed by some as non-standard and presumably is proscribed in geometry and mathematics because it's an oxymoron; it’s a portmanteau word, the construct being slant + (perp)endicular.  It may be useful however in commerce or engineering where it might be used to describe something like a tool with a shaft which at some point assumes an oblique or skewed angle.   So it’s there to be used and slantindicular should be applied to stuff which is neither wholly nor fully slanted and in architecture, such structures are numerous.  In commerce, it could be used as a noun.

The noun slant by the 1650s was used to mean “an oblique direction or plane” and began in geography & civil engineering (of landforms, notably ski-slopes), developed from the verb or its adjective.  The now familiar (in the Fox News sense) meaning “way of regarding something, a mental bias” dates from 1905 while the derogatory slang sense of “a person of Asian appearance” came into use some time in the 1940s, a direct descendent from the earlier "slant-eyes", documented since 1929.  The verb slant is documented since the 1520s in the sense of “obliquely to strike (against something)”, an alteration the late thirteenth century slenten (slip sideways), the origin of which is murky but etymologists have concluded it came (via a Scandinavian source (noting the Swedish slinta (to slip)) and the Norwegian slenta (to fall on one side), from the Proto-Germanic slintanan.  The intransitive sense of “to slope, to lie obliquely” was in use by the 1690s, while the transitive sense of “to give a sloping direction to” had emerged by the early nineteenth century.  As early as the late fifteenth century forms were in use as an adverb, the adjectival use attested from the 1610s.  The technical use in literary theory as “poetic slant rhyme” was first used in the mid 1920s (assonance or consonance) although such lines had appeared for centuries, used sometimes deliberately as a device, sometimes not.  In the following stanza by English poet Peter Redgrove (The Archaeologist, published in Dr Faust's Sea-Spiral Spirit (1972)), the second and third lines contain a form of slant rhyme while the first and fourth have pure rhymes:

So I take one of those thin plates
And fit it to a knuckled other,
Carefully, for it trembles on the edge of powder,
Restore the jaw and find the fangs their mates.

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While it’s unlikely volumes of the poetry of Emily Dickinson (1830–1886) sit upon the bookshelves of those members of the Fox News audience who have bookshelves, they likely would concur with her words: “Tell the truth but tell it slant.”  “Slanted reporting” has become something which in recent years has attracted much attention (and much hand-wringing by the usual suspects) as an increasingly polarization of positions has been alleged to be a feature of political discourse in the West.  There is little doubt the effect (as reported) is obvious but there’s some debate about both the mechanics and the implications of the phenomenon.  As long ago as 2018, a study found that although the tenor and volume of things on X (formerly known as Twitter) was found to be increasingly toxic and surging, the number of active users engaged in these political polemics was found to be tiny and their effect was distorted by (1) the huge number of tweets they tended to post, (2) the propensity of their fellow-travelers to re-tweet and (3) the use of bots which were more prolific still.  If anything, recent voting patterns suggest it would seem the views of the general population appear to be trending away from the extremes towards the more centralist positions offered by independents or small-parties, something most obvious in Australia where compulsory voting exists.  Outfits like Fox News offer a slanted take on just about everything (and promote country & western music which truly is inexcusable) but this is something which has been identifiable in the news media as long as it’s existed and their blatant bias is hardly subversive or threatening, simply because it is so blatant.  What was most interesting in what emerged from the recent defamation suit filed by Dominion Voting Systems against Fox News suggested the network’s stance on things was motivated more by the financial imperative than ideological purity.  Intriguingly, what some analysts concluded was that if the universe shifted and the Fox News audience transformed into a bunch of seed-eating hippies, there would follow Fox’s editorial position, the slant being towards the advertising revenue rather than a particular world view.  Of course, there are some slants which are unalterable and dictated by ideological purity but with commercial media, it’s likely sometimes cause is confused with effect.

The Leaning Tower of Pisa (left) and Lindsay Lohan in The Parent Trap (1998) in front of London’s perpendicular Big Ben (1859) (right).  The architect’s original name for the latter was a typically succinct “Clock Tower”, chosen because it housed the “Great Bell of the Great Clock of Westminster” but it was in 2012 renamed “Elizabeth Tower”, marking the Diamond Jubilee of Elizabeth II (1926-2022; Queen of the UK and other places, 1952-2022), something little noted by Londoners or those beyond who continue to prefer the nickname “Big Ben” although strictly speaking that’s a reference only to the “Great Bell” a 13.5 ton (13.7 tonne) casting in bell metal (a bronze which is an alloy of about 77% copper & 23% tin).  The origin of the nickname is contested but there are no romantic tales, all the possible inspirations being worthy white men as was the Victorian way.

Although in Italy alone there are seven leaning towers (three of which stand (ie lean) in Venice), it’s the torre di Pisa (Tower of Pisa) which is by far the best-known and a frequent Instagram prop.  Built between 1173-1372, the structure in the Piazza del Duomo (Pisa’s Cathedral Square) is the campanile (the freestanding bell tower) of the adjacent Pisa Cathedral and the famous lean of some 4^o (actually somewhat less than its greatest extent after more than a century of compensating engineering works) was apparent even during construction, the cause the softness of the sub-surface.  That geological feature has however contributed to the tower’s survival, the “rubber-like” sponginess below acting to absorb movement and despite a number of severe earthquakes in the region over the centuries, the tower remains.  It is of course known as the leaning tower than a sloping, oblique or slanted tower, probably because of the conventions of use which evolved in English.

The words “sloping”, “oblique”, “slanted”, & “leaning” all describe something not vertical or horizontal there tend to be nuances which dictate the choice of which to use.  Sloping generally is used of something which inclines or declines at a gentle or continuous angle, the implication being of a gradual or smooth transition from elevation to another, such as the way a hillside rises gradually rises to its summit.  Oblique is mostly a matter of specific angles and is thus common is mathematics, geometry and engineering.  Again, it’s a reference to something neither parallel nor perpendicular to a baseline but it tends to be restricted to something which can be defined with an exact measurement; in geometric or technical use, an oblique line or angle is one neither 90^o nor perfectly horizontal.  Slanted describes something positioned at a diagonal, often used to imply a more noticeable or sharp angle but also is widely used figuratively, metaphorically and in idiomatic phrases.  Leaning refers to something tilted or positioned at an angle due to external pressure, the object in an unstable position and in need of support.  The implication carried is that something which “slants” is designed thus to do while something which “leans” does so because of some design flaw or unexpected external force being applied so it’s the leaning and not the sloping tower of Pisa, even though the structure has assumed quite a slope.

Slanting Engines

On a slant: Diagram of the mounting of the M194 straight-six engine in the Le Mans winning Mercedes-Benz 300 SL (W194) canted at a 40^o slant (left); the Mercedes-Benz M196 straight-eight engine schematic (centre) and installed in a 1954 W196R "Streamliner" at a 53^o slant (right).  The two large donut-like objects at the front are the inboard, finned brake drums; at the time, the engineers maintained disk brakes were "not yet ready for use". 

There are “slant” engines and they exist in three configurations.  The first is simply a conventional in-line engine (straight-six, straight-eight etc) which, when installed in a vehicle, is fitted with the block canted to the left or right, the objective being a lower hood line which means a better aerodynamic outcome.  A classic example was the Mercedes-Benz W196R Formula One racing car (1954-1955) in which the straight-eight was canted to the right at a 53^o angle, the technique carried over when the same structure was used to produce the W196S (1955) used to contest the World Sports Car Championship.  Rather opportunistically, the W196S was dubbed the 300 SLR (one of which in 2022 became the world's most expensive used car, selling at a private auction for US$142 million) as a form of cross promotion with the 300 SL (W198, 1954-1956) Gullwing then in production, even though the two types shared little more than nuts, bolts and a resemblance.  The 300 SL did however also have its straight-six engine sitting at a slant, this time canted at a 50^o angle and although the factory never published an estimate of the reduction in drag, it’s long been presumed to be “at least several percent”.  Another advantage of the configuration was it made possible the use of “long-tube” runners for the induction system, taking advantage of the properties of fluid dynamics to permit them to be tuned either for mid-range torque or top-end power.  The concept used math which had been worked out in the nineteenth century and had often been used in competition but it wasn’t until 1959 when Chrysler in the US released their picturesque induction castings that the system, imaginatively named the “Sonoramic”, reached a wider audience.

Chrysler Slant Six (170 cid, 1963) schematic.

The “true” slant engines were those with a slanted block atop an otherwise conventional arrangement of components, the best known of which was Chrysler’s long-serving “Slant Six”, produced in displacements of 170 cubic inch (2.8 litre, 1959-1969), 198 cubic inch (3.2 litre, 1970-1974) and 225 cubic inch (3.7 litre, 1960-2000).  The block of the Slant Six was canted to the right at a 30^o and like Mercedes-Benz, Chrysler took advantage of the space created to the left to produce some wide induction runners, the most extravagant those used by the special Hyper Pack option package which used a four barrel carburetor, enabling the engine to produce power which made it competitive with many V8 powered machines.  Although the name “Slant Six” became famous, it was only in the mid-sixties it caught on, Plymouth originally calling the thing a 30-D (a reference to the a 30^o slant), hardly very catchy and something to which only engineers would relate and Slant Six was soon preferred although the aficionados really like “tower of power” and the engine even today still has a devoted following.

Chrysler Slant Six with Hyper Pak in 1962 Plymouth Valiant V-200.

Chrysler didn’t restrict the Sonoramics to the big-block V8s, using it also on the short-lived (1960-1962) Hyper Pak performance option for the both 170 cubic inch (2.8 litre, 1959-1969) and 225 cubic inch (3.7 litre, 1987-2000) versions of the Slant Six, the engineers taking advantage of the space afforded by the canted block to permit the curvaceous intake runners nearly to fill the engine bay.  The Hyper Pak wasn't seen in showrooms but was available as an over-the-counter kit (literally a cardboard box containing all necessary parts) from Dodge & Plymouth spare parts departments and its life was limited because it became a victim of its own success.  Although less suitable for street use because it turned the mild-mannered straight-six into something at its best at full throttle, in the race events for which it was eligible it proved unbeatable, dominating the competition for two years, compelling the sanctioning body cancel the series.

Manifold porn: The Slant Six's angle meant there was much space available to the left and a range of intake manifolds followed, some of which remain available to this day.  Using variations of the sonoramic tuning, manifolds were produced for single, two & four barrel carburetors and between 1965-1968, Chrysler's Argentine operation produced the Slant Six in a version with twin single barrel carburetors.  The use of the properties of fluid dynamics to gain power or torque as desired quickly was adopted by the industry as an engineering orthodoxy.

Some myths seem to have become attached to the Hyper-Pak.  What seems to be true is the original kit, sold in 1960 for the 170 engines used in competition, was a genuine homologation exercise and as well as the intake manifold & Carter AFB four barrel carburetor, it included all the internal parts such as the high-compression pistons, the high-lift camshaft and the valve train components needed to support the consequently higher engine speeds.  Because the competition rules allowed modifications to the exhaust system, on the track the cars ran tubular steel headers which fed an open exhaust, terminating in the racers' preferred “dump pipe”.  After the requisite number of “complete” kits were sold, thus fulfilling the homologation demands, the kits were reconfigured and included only the “bolt-on” parts such as the induction system and a camshaft which, while more aggressive than the standard unit, wasn’t as radical as the one used on the track but could be used in conjunction with the standard valve train and Chrysler’s TorqueFlite automatic, thus expanding the Hyper-Pak’s appeal.

At the same time, the availability was extended to the larger 225 which between 1961-1963 was also available with an aluminum block, thus becoming one of the small number of engines configured with the combination of an aluminum block with a cast-iron head.  US manufacturers were at the time aware the trend was for cars to continue getting bigger so they were interested in ways to reduce weight.  However, despite saving some 70 lbs (32 KG), Chrysler’s aluminum block was, like General Motors’ (GM) 215 cubic inch (3.5 litre) V8, short-lived (though the V8 after being sold to Rover enjoyed a long, lucrative and prolific second life, not finally laid to rest until 2006) for not only were teething troubles encountered with the still novel method of construction, the accountants made clear using cast iron was always going to be cheaper so the industry just accepted weight gain and whenever required, increased displacement to compensate, an approach which persisted until the first oil shock of the early 1970s.

1970 Dodge Challenger (1970-1974) with 225 Slant Six.

Until 1973, both the Challenger & the corporation's companion pony car (the Plymouth Barracuda (1964-1974)) was available with the Slant Six (198 & 225) although the fitment rate was under 10%, unlike the early pony cars (Ford Mustang, Chevrolet Camaro and the early Barracudas) where the six-cylinder versions would at times be close to 40% of production.  Many of the surviving Slant Six Challengers & Barracudas have been "re-purposed" as clones of the more desirable versions with big-block V8s.

Although it was the longer lived 225 version which gained the Slant Six its stellar reputation for durability and the ease with which additional power could be extracted, there's always been a following for the short-stroke 170 because of its European-like willingness to rev, the characteristics of the over-square engine (unique among the slant-six's three displacements (170-198-225)) unusually lively for a US straight-six.  Despite some aspects of the specification being modest (there were only four main bearings although they were the beefy units used in the 426 cubic inch Street Hemi V8), for much of its life it used a tough forged steel crankshaft and high-speed tolerant solid valve lifters; it proved a was a famously robust engine and one remarkably tolerant of neglect.  Despite that, after the Hyper Pak affair, Chrysler in the US showed little interest in any performance potential, knowing the US preference for V8s, something which doomed also Pontiac's short-lived single overhead camshaft (SOHC) straight-six (1966-1969).  A version of the 225 with a two-barrel carburetor (rated at 160 horsepower, an increase of 15 over the standard unit) was offered in some non-North American markets where V8 sales were not dominant and it proved very popular in South Africa, Australia, New Zealand and Central & South America but only when tighter US emission regulations forced its adoption did a 225 with a two barrel carburetor appear in the home market though there it was installed to restore the power losses suffered after the emission control plumbing was added rather than seek gains.

Pontiac Trophy 4 cutaway.

Making a straight-eight or V8 by combining two in-line fours has been done a few times and many have been successful (although Triumph managed to create a truly horrid one for the otherwise lovely Stag).  Less common is making a four from an eight but that’s what Pontiac did when they conjured their 194.5 cubic inch (3.2 litre) four by using one bank of their 389 cubic inch (6.4 litre) Trophy V8 and it was (just about) literally cut in half, meaning the cylinders were canted to the right by 45^o (the V8 obviously in a conventional 90^o configuration.  To emphasize the family connection with the highly regarded Pontiac Trophy V8, the smaller offspring was called the Trophy 4 (although it was at time also dubbed the Indy 4 or Indianapolis 4 which even at the time sounded ambitious).  It did work and the economic advantages for the manufacturer (use of common components and the same assembly line) were compelling but the limitations inherent in a four-cylinder of such a large displacement were apparent in the rough-running and wear on critical parts and it was available only between 1961-1963, only in the compact Tempest.

Diagram showing balance shaft locations.

Large displacement four cylinder engines have been built.  Fiat in 1910 built two of their S76s to contest the world LSR (land speed record) and they were an hefty 28.4 litres (1730 cubic inch), the “Beast of Turin” using its then impressive 290 horsepower (216 kW) to attain a one-way speed of 132.27 mph (213 km/h) but, because it was not possible for the team to make the “return run” (ie in the opposite direction) within the stipulated one hour, the LSR remained with the Blitzen Benz which in 1909 had set a mark of 125.94 mph (202.65 km/h).  On land, never again would anyone build a four with the capacity to match the Beasts of Turin but units with displacements approaching 5.0 litres (305 cubic inch) were not uncommon during the inter-war years.  However, the technology of the internal combustion engine (ICE) greatly advanced during World War II (1939-1945) and one consequence of that was engine speeds rose and less displacement was required for a specific output, both factors which conspired to make the big fours unfashionable.  They did however make a comeback in the 1970s when the clever trick of “balance shafts” enabled the inherently chronic second order harmonic vibrations to be “dampened out” and Porsche between 1991-1995 produced a 3.0 litre (183 cubic inch) range which used the technique.  The balance shaft was invented early in the twentieth century by English engineer Frederick Lanchester (1868–1946) but it was Mitsubishi which in the 1970s patented their “Silent Shaft” system and although Porsche developed their own version, they worked out the Japanese design was superior so used that instead, paying Mitsubishi a small royalty (under US$10) for each one installed.  A balance shaft uses two counterweights (looking something like small hockey pucks with the shaft running through them), set some 1½ inches (40 mm) apart and turns at twice the engine-speed.  With one shaft mounted high on one side of the engine and the other low on the opposite side, the pair counter-rotates, balancing the large reciprocating mass.