Orthogonal

Orthogonal (pronounced awr-thog-uh-nl)

(1) Of, pertaining to or involving right angles; perpendicular

(2) In mathematics (sometimes as orthographic), pertaining to or involving right angles or perpendiculars.

(3) In mathematics, of a system of real functions defined so that the integral of the product of any two different functions is zero; of a system of complex functions defined so that the integral of the product of a function times the complex conjugate of any other function equals zero.

(4) In mathematics, of two vectors having an inner product equal to zero.

(5) In mathematics, of a linear transformation defined so that the length of a vector under the transformation equals the length of the original vector.

(6) In mathematics (and applied fields such as engineering or statistics), of a square matrix defined so that its product with its transpose results in the identity matrix.

(7) In crystallography, referable to a rectangular set of axes.

(8) Figuratively, something having no bearing on the matter at hand; independent of or irrelevant to another thing or each other.

(9) In art, (1) the descriptor of the lines of perspective which can be mapped onto an image pointing to the vanishing point & (2) in the literature of art criticism a technical term which refers to work consisting exclusively of horizontal or vertical line and thus angles which, if they exist, are right angles.

1565–1575: From (the now obsolete) orthogonium (right triangle), from the French orthogonal, from either the Late Latin orthogōnium & orthogōnālis, from the Latin orthogōnius (right-angled).or directly from the Greek orthogṓnion (neuter) (right-angled), the construct being ortho- + -gōn(ion) + -al.  Ortho- (straight, correct; proper), was from the Ancient Greek ὀρθός (orthós), from the Proto-Hellenic ortwós, from the primitive Indo-European hr̥dwós, from herd- (upright) and was cognate with the Latin arduus and the Sanskrit ऊर्ध्व (ūrdhvá).  The –gon element was from the Ancient Greek γωνία (gōnía) (corner, angle), from the primitive Indo-European ǵónu (knee).  The -al suffix was from the Middle English -al, from the Latin adjectival suffix -ālis, or the French, Middle French and Old French –el & -al.  It was use to denote the sense "of or pertaining to", an adjectival suffix appended (most often to nouns) originally most frequently to words of Latin origin, but since used variously and also was used to form nouns, especially of verbal action.  The alternative form in English remains -ual (-all being obsolete).  Orthogonal is a noun & adjective, orthogonality & orthogonalization are nouns and orthogonally & orthonormal are adverbs; the noun plural is orthogonals.

As adjectives, orthogonal & orthographic are synonymously and the choice is dictated by preference, habit or the rhythm of the text although, to avoid confusion, they probably shouldn’t both be used in the same document.  The Ancient Greek ὀρθογώνιον (orthogṓnion) and the Classical Latin orthogonium originally denoted a rectangle and it was in this sense the words were used by the early mathematicians although the use was later extended to mean a right triangle.  By the twelfth century (especially among engineers and architects) the post-Classical Latin orthogonalis came to mean a right angle or something related to a right angle.  In the modern era, in science and mathematics, derived forms have been coined as required (biorthogonal, psuedo-orthogonal et al) and there’s also the mysterious semiorthogonal which would seem oxymoronic given orthogonal is a description of a mathematically defined absolute.  In figurative use, orthogonal is used to suggest something is unrelated or irrelevant to whatever is being discussed but because it’s so rarely used outside of mathematics, engineering, architecture or art criticism, it’s probably a term to avoid though it may be worth a point or two in Philosophy 101.

Lindsay Lohan in an unusual cage cutout top, the lines assuming or relaxing from the orthogonal as the body moves (maybe an instance of "a shifting semiorthogonal"), The World's First Fabulous Fund Fair in aid of the Naked Heart Foundation, The Roundhouse, London, February 2015.  An opportunity was missed by not adding a sympathetic clutch purse.

Richard Nixon, the Franklins & the Orthogonians

When Richard Nixon (1913-1994; US president 1969-1974) attended Whittier College in California (1930-1934), it was still formally affiliated with the Religious Society of Friends (the Quakers), a link it would maintain until the post-war years.  However, in many ways it was little different to wholly secular institutions in the US (except that one hour a day in chapel was mandatory), including the fraternities and sororities, the still almost exclusively single-sex, student-run societies which were established on many a basis and have evolved variously although a number of the male-only ones often attract attention related to their epic levels of alcohol consumption.  As was the case with many colleges until recent decades, many of those which Richard Nixon found when he arrived had been formed as literary societies and while there were four sororities (for women), there was but one fraternity.

That was the Franklin Society which in 1921 had been the first fraternity founded at Whittier College, beginning as a literary society that based itself on the "virtues" espoused by US founding father and polymath (and confessed Freemason) Benjamin Franklin (1706-1790).  Nixon, then unpolished and obviously a shop-keeper’s son, thought them snobby and elitist, an opinion either form or reinforced when the Franklins rebuffed attempts to join and readily he accepted the suggestion be assume the presidency of the fraternity formed by other students resentful at being rejected by the Franklins.  This was the Orthogonians, the name (based on the now standard translation “right angles”) meaning “the straight shooters”, their motto an earthy “beans, brains, brawn and bowels”.  The Orthogonians did not enjoy the black tie lifestyle of the Franklins and weren’t invited to the best parties but several of Nixon’s biographers have traced from his fraternity experience many of the characteristics which would remain identifiable throughout this political career.  He learned that in life there are few stars but many supporting players and the man who can align himself with their interests you can gain their loyalty, something of real practical value in systems where everyone has one vote; it was the origin of his idea that elections and contests of ideas can be won by being appealing to the “silent majority”, something which would emerge as a political strategy during his presidency.  It taught him also that being hated was no obstacle to political success as long as one was hated by the right people, something he proved by beating the Franklin’s nominee for the position of student body president.  To this day, the Frankin’s website still boasts: “Among those who have been denied membership to this exclusive society is former president Richard Nixon.”  The Orthogoian Society still exists.

The master and the apprentice: Donald Trump and Richard Nixon, Houston, Texas, 1989.  It’s said the subject of Iran was raised in their discussions.

Some biographers have made much of the Franklin-Orthogonian contrast in the making of Nixon the younger.  In Nixonland (2008), Rick Perlstein’s (b 1969) thesis was that between 1965-1972, Nixon crafted a national conflict by exploiting the the mutual fear and hatred between the country’s elite Franklins and the “ordinary people, the Orthogonians.  Some criticized the approach but Nixonland was a vivid approach to the era in which the divisions in the US became more exposed than they had been for a century and which was a prelude to the cross-cutting cleavages which have for decades characterized the country’s politics.  Nixon didn’t invent the politics of resentment but he expressed them in a language more easily understood by even the unsophisticated and more offensive than ever to those he labeled “the elites”.  In their own ways, to their radically different constituencies, Bernie Sanders (b 1941; senior US senator (Independent, Vermont) since 2007) and Donald Trump (b 1946; US president 2017-2021) are both inheritors of the Nixon legacy, two Franklins telling the Orthogonians they’re here to help.

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.

Fabulous

Fabulous (pronounced fab-yuh-luhs)

(1) Exceptionally good or unusual, wonderful or superb; fashionable, glamorous (which pedants insist is informal but it’s long been the standard meaning).

(2) Almost impossible to believe; incredible.

(3) In slang or as a euphemism, gay or pertaining to gay people; camp, effeminate ("a fabulousity" suggested as a collective noun for gay men but it never caught on) .

(4) In slang, fashionable, glamorous.

(5) Of or about fables; stories wholly or substantially of the imaginary and known of through myth or legend; something in the record known to be unhistorical.

Circa 1550: From the Late Middle English fabulous & fabulose, from the Latin fābulōsus (celebrated in fable; rich in myth), the construct being fābul(a) (a story, a tale) + -ōsus (the adjectival suffix).  The –ōsus suffix (familiar in English as –ous) was from Classical Latin from -ōnt-to-s from -o-wont-to -s, the latter form a combination of two primitive Indo-European suffixes: -went & -wont.  Related to these were –entus and the Ancient Greek -εις (-eis) and all were used to form adjectives from nouns.  In Latin, -ōsus was added to a noun to form an adjective indicating an abundance of that noun.  As a literary genre (and some fables came from oral traditions) fables were stories told usually to make some moral point or illustrate the consequences of one’s actions and while they could sometimes involve fantastical creatures like winged stallions or unicorns, sometimes they involved fictional characters who were mere flesh & blood and even a multi-volume, epic-length novel like Don Quixote (1605-1615) by Miguel de Cervantes circa 1547–1616) can be thought a fable.  Fabulous is an adjective, fabulousness & fabulosity are nouns and fabulously is an adverb; the use is the plural is rare but both fabulousnesses & fabulosities exist.  There is some evidence of use in the gay community of fabulous as a (non-standard) noun, sometime in the form “uber-fabulous” although that construction is also used generally as an adjective of especial emphasis.

Looking fabulous: Lindsay Lohan Fabulous magazine, August 2010.

The original sense was “of or pertaining to fable” and dates from the 1550s.  The now familiar meaning shift began as early as the turn of the seventeenth centuries when the word was recorded to convey the sense of “incredible” which soon extended to “enormous, immense; amazing” and by the mid-twentieth century it was used almost exclusively to mean “marvelous; wonderful, superb”.  The clipping to create the slang “fab” was in used by at least 1957 and use spiked after 1963 when the alliterative “fab four” was used to describe the pop group, The Beatles.  When in 1965 revising Henry Fowler’s (1858–1933), A Dictionary of Modern English Usage (1926), Sir Ernest Gowers (1880–1966) maintained his predecessor’s disapproval of much that was a bit too modern, noting that correctly fabulous meant “…mythical, legendary, but was long ago extended to do duty as an adjective for something that is real but so astonishing that you might not think it was legendary if you did not know better.”, adding that it had “…become fabulously popular as a term of eulogy or allure.”  He seemed though to suspect it might be a “fad word”, noting it and its contracted forms “fab” & “fabs”, like “fantastic”, were perhaps the latest “…in that long list of words which boys and girls use for a time to express high commendation and then get tired of, such as, to go no farther back than the present century, topping, spiffing, ripping, wizard, super, posh, smashing.”  Decades on however, fabulous seems to have endured in its contemporary uses and even the portmanteau adjective fantabulous (the construct being fanta(stic) + (fa)bulous) has survived in its niche.  Fabulous probably gained a new lease of life when it was in the late 1960s picked up by the gay community which has used it even as a noun and it remains an essential element in the camp vocabulary.  Unless it’s between scholars, those wishing to convey the original meaning should probably use terms such as “fabled” or “mythological” rather than fabulous and even “legendary” can be ambiguous because it’s now often used to mean something like “famous” or “very well-known”.

Lindsay Lohan in an unusual cage cutout top, the lines assuming or relaxing from the orthogonal as the body moves (maybe an instance of "a shifting semiorthogonal"), The World's First Fabulous Fund Fair in aid of the Naked Heart Foundation, The Roundhouse, London, February 2015.  An opportunity was missed by not adding a sympathetic clutch purse.

George W Bush, Condoleezza Rice & Colin Powell.

The phrase “the fabulous invalid” refers to live theater & stage productions generally, the use derived from a 1938 stage play of that name by George S Kaufman (1889-1961) and Moss Hart (1904-1961) which traced the that follows the seesawing fortunes of a fictitious Broadway theater between 1900-1930.  In a touching irony, while the play was barely a modest success and not highly regarded by its authors, the title has endured as a synonym for the theatre.  George W Bush (George XLIII, b 1946; US president 2001-2009) who (admittedly unwittingly) contributed more than most to coining new words & novel grammatical structures, probably wasn’t deliberately alluding the original meaning of fabulous when he used it to describe the performance of his first foreign minister, Colin Powell (1937–2021; US secretary of state 2001-2005) but if considered thus it certainly reflected his view that the general’s favorable public image reflected more myth than reality and he’d prefer a secretary of state who both ticked a few boxes and was more attuned to his brutish world-view.  In Dr Condoleezza Rice (b 1954; US secretary of state 2005-2009) he certainly got that but in the run-up to the invasion of Iraq, whatever might have been his better judgment, the general did his job because, as Field Marshall Wilhelm Keitel (1882–1946; head of Oberkommando der Wehrmacht (OKW), the Nazi armed forces high command) put it at the Nuremberg Trial (1645-1946): “For a soldier, orders are orders.”  His flirtation with politics is a fable and story of Condoleezza Rice’s career in government even more so: a cautionary tale of what can happen when a nice young lady from a good family gets mixed up with an unsavory crowd (Bush, Cheney, Rumsfeld et al).

White House transcript of press conference assembled when the president met with Colin Powell and Richard Armitage (b 1945; US deputy secretary of state 2001-2005) at his ranch in Crawford, Texas, Wednesday, 6 August 2003:

THE PRESIDENT: First, it's been my real privilege and honor to welcome the Secretary of State back to Crawford. He and Dick Armitage came, and we spent yesterday evening and this morning talking about our country's desire to promote peace and freedom, our obligations as a prosperous and strong nation to help the less fortunate. And we had a good strategy session, and now we're about to go out and brand some cows -- well, not exactly. (Laughter)

QUESTION: Sir, you've seen the report that Secretary Powell and Secretary Armitage are going to leave at the end of this administration. Do you expect them to stay on if there is a second Bush administration? Would you like them to?

THE PRESIDENT: Well, first things first, we hope there is a second Bush administration. And I will work hard to convince the American people that their confidence in me is justified. And we'll deal with it at the right time.  Listen, this guy has done a fabulous job. Washington, particularly in August, is a dangerous period -- a dangerous time, because there's a lot of speculation. And all I can tell you is, the man flies to Crawford and we spend a good 24 hours talking about how we're going to work together to make the world a better place.

QUESTION: But, Mr. President, you said, we'll deal with it…

THE PRESIDENT: Yes, Elizabeth.

QUESTION: We'll deal with it at the right time. That isn't "yes".

THE PRESIDENT: Deal with what at the right time?

QUESTION: With whether Secretary Powell will serve in a second term. Is that, "yes" or "no"? I mean, are you going to offer him a spot in the second term?

SECRETARY POWELL: I don't have a term. I serve the President. (Laughter)

QUESTION: No, but the President…

THE PRESIDENT: Elizabeth, look, first things first, and that is, we've got a year-and-a-while during my first term to make the world a more peaceful place and we'll deal with it. Washington loves speculation. Clearly, you love speculation. You love it. You love to speculate about…

QUESTION: It wasn't my story. (Laughter.)

THE PRESIDENT: Let me finish, please; let me finish. You love to speculate about whether so-and-so is going to be a part of the administration or not. And I understand the game. But I have got to do my job, and I'm going to do it. And I'm going to do it with the Secretary of State. And the fact that he is here in Crawford, Texas, talking about issues of importance, should say loud and clear to the American people that he's completely engaged in doing what he needs to do, and that is, serve as a great Secretary of State.

QUESTION: Do you want to serve more than four years, Mr. Secretary?

SECRETARY POWELL: I serve at the pleasure of the President, and this is all August speculation with no basis in fact. There was no basis for this story to begin with, and we're doing our jobs together.

THE PRESIDENT: All right. We're going to get a burger. Thank you.

Pood

Pood (pronounced pood or poot (Russian))

(1) An old Russian unit of mass, equal to 40 Russian funt, or about 16.38 kg (36.11 lb).

(2) A Russian unit of mass used for kettlebells (a hand-held weight used in physical training and competition), now rounded off to 16 kg (35.274 lb pounds).

(3) In computing, as POOD, (principle of orthogonal design), a model of database design with parameters designed to avoid redundancies and duplicated routines.

1100s: From the Russian пуд (pud), from Low German or Old Norse pund (pound) (unit of weight and measure), from the Late Latin pondo (by weight; in weight), from the Classical Latin pondus (weight, heaviness, density), From the Proto-Italic pondos, from the primitive Indo-European spénd-os & pénd-os, from spend- and pend-..  A doublet of pound, the alternative spelling was poud.  Pood is a noun; the noun plural is poods (pudi or pudy in Russian).

Instructions for using a 1 pood kettlebell.

Under comrade Stalin (1878-1953; Soviet leader 1924-1953), the pood, like other units of weight defined by the system used in Imperial Russia, officially was abolished in 1924 but, beyond the big cities, the old ways remained in wide use until the 1950s and, for informal transactions (which at times constituted a substantial part of the Soviet economy) it really went extinct only as the older generations died off.  One quirk however remains, the weight of the traditional Russian kettlebells (a hand-held weight used in physical training and competition), cast in multiples and fractions of 16 kg (the metric version of the pood), the 8 kg ketterbell a ½ pood, a 24 kg a 1½ pood.  Informally, among traders, bulk agricultural communities such as grain, potatoes and beets are sometimes expressed in poods, reputedly because the sacks used in retail distribution are still made in sizes in which quantities such as 8, 16, 32, 48 & 64 kg can conveniently be bagged.

1 pood kettlebells in the shape of Russian President Vladimir Putin’s head, Heavy Metal Shop, Moscow.

Had all the relevant evidence been presented in court when Albert Speer (1905–1981; Nazi minister of armaments and war production 1942-1945) was tried before the International Military Tribunal (IMT) at Nuremberg (1945-1946) he’d likely have been hanged but as it was, convicted on counts 3 (war crimes) and 4 (crimes against humanity) he was sentenced to twenty years, most of which were served in Spandau Prison.  In there, he wrote the notes for what became his not wholly reliable but still valuable memoir and a prison diary.  Selectively edited, The Spandau Diary (1975) was one of the minor classics of the genre, not least because it was probably more helpful than all the many reports by psychologists and psychiatrists in assessing whether his fellow inmate Rudolf Hess (1894–1987; Nazi deputy führer 1933-1941) was mad, either during his trial or subsequently.  It was also a rich source of the type of anecdotes which distinguish prison journals, one of which came from a Soviet guards who, after Speer observed to him the new Soviet prison director “didn’t seem so bad”, recited an old Russian proverb: Человека узнаешь, когда с ним пуд соли съешь which he translated as “you do not know a man until you have used up a pood of salt with him”.  Speer, then in the fourteenth year of his sentence, was interested enough to look up just how much a pood weighed but didn’t comment further.  As other prison diaries have noted, guards provide much practical advice.  A year earlier, resting in bed with a swollen knee, he mentioned to one of the Soviet guards that the Russian doctor had prescribed two aspirins a day.  Knowing the guard to be “a veterinarian on the side”, he asked how a horse with a swollen knee should be treated.  “If horse cheap, shoot dead.  If good horse, give aspirin” he was told.  Again, Speer added no comment.

Khlebosolyn: Young ladies in traditional dress presenting bread and salt to a visitor.

Quite how long it would take two chaps to work their way through 16 kg odd (35 lb) of salt is geographically and culturally variable.  In a modern Western household, that quantity of salt would typically last years and while after that long two people should be well acquainted with each other’s foibles, in pre-Modern Russia, a pood might have been absorbed more quickly.  For one thing, in the pre-refrigeration age, salt was often used in bulk to cure and preserve food including meant and fish and that was sometimes necessary even in Russia’s colder parts and there was also much boiling of food in salt water.  Prized since Antiquity, highly taxed in Imperial Russia and therefore expensive, salt was also an important part of cultural tradition.  A ritual invoked when greeting important guests was to present on the table a loaf of bread, placed upon a rushnyk (an elaborately embroidered cloth), atop which was placed a salt cellar.  The ceremony is the origin of the Russian word khlebosolny (literally “bready-salty”) which expresses someone’s hospitality, bread and salt traditional symbols of prosperity and good health.  So, salt consumption in old Russia was quite a bit higher than in modernity (not counting the high levels in processed food) and the consensus is the proverb probably means people truly don’t know anyone until they’ve spent a year or more together.

Pood is wholly unrelated to poodle (a dog breed dating from 1808), from the German Pudel, a shortened form of Pudelhund (water dog), the construct being the Low German Pudel (puddle) (related to pudeln (to splash) and the Modern English puddle) + the + German Hund (hound; dog).  The origin in German is thought related to the dogs originally being used to hunt water fowl, but in England and North America, it was always a term for an undersized fancy or toy dog with long, curly hair.  The essentially decorative qualities of the diminutive canine meant that in UK the figurative sense of "lackey" emerged in 1907, perhaps derived from the British army slang “poodle-faker”, defined in the slang dictionaries of the age as “an ingratiating” but thought always used euphemistically as a gay slur.  Despite legislative reform which removed all legal prohibitions on homosexual acts, that sense survived into twenty-first Australia to be used on the floor of the parliament by Julia Gillard (b 1961; Australian prime minister 2010-2013), later famous for her “misogyny speech” which deplored sexism and sexist language (when aimed at her).  In 2009, she used the imagery of “mincing” & “poodle” as a slur against another (male, married and with four children) parliamentarian who was admittedly really annoying and needlessly neat and tidy but it was a slur nonetheless.

The mincing poodle tapes.

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.

Duumvirate

Duumvirate (pronounced doo-uhm-ver-it)

(1) A coalition of two persons holding the same office at the head of government.

(2) The office or government of two such persons.

1656: From the Latin duumvirātus (one of two officers or magistrates jointly exercising the same public function), the construct being duumviri (the office held in the Roman Republic by two joint magistrates and plural of duumvir) + -atus.  Duumviri was from the Old Latin, the construct being duum (of two) + vir (man) and a duumvir was one who served in the office of a duumvirate.  The Latin suffix -ātus was from the Proto-Italic -ātos, from the primitive Indo-European -ehtos.  It’s regarded as a "pseudo-participle" and perhaps related to –tus although though similar formations in other Indo-European languages indicate it was distinct from it already in early Indo-European times.  It was cognate with the Proto-Slavic –atъ and the Proto-Germanic -ōdaz (the English form being -ed (having).  The feminine form was –āta, the neuter –ātum and it was used to form adjectives from nouns indicating the possession of a thing or a quality.  In Ancient Greece, a similar polity was a diarchy, the construct in the Ancient Greek being δι- (di-) (double) + -αρχία, (-arkhía) (ruled).

In political science, a diarchy (Greek) or duumvirate (Latin) is a form of government characterized by co-rule, two people ruling a polity together, either lawfully or by collusion & force and such leaders can be styled as co-rulers.  Inventions in language have occurred such as biarchy and tandemocracy though none became common use, unlike co-regency, used still to describe a monarchy temporarily controlled by two.  Under the Raj, diarchy was often used to refer to the system of “shared rule”, a colonial fix of which the British were the cynical masters.  Native Indian representation in government had long been a feature of British India and it was formalized in the Indian Councils Act (1892), the powers further devolved in the Government of India Acts (1919 (implementing the Montague-Chelmsford reforms) & 1935).

Under the Raj, provincial governments included British members (executive councilors) and Indian members (ministers from the legislative council).  So that administrative authority could be conferred on Indian members, the diarchy was introduced and with it the concept of transferred and reserved subjects.  The transferred subjects included law and order, revenue & justice; the reserved subjects included education & public health etc so in this way, so typical of British colonial rule, Indians gained control over large parts of the government which dealt directly with the people while authority over critical matters (money, defense, foreign affairs, internal order) remained under the purview of British executive councilors.  Diarchy operated in the Indian provinces between 1921- 1937 before being replaced by provincial autonomy in 1937.

However, those uses on the sub-continent reflect the post-classical practice to use both duumvirate and diarchy to describe just about any arrangement where the highest office or institution in a state (and often other places too) is not in the hands of a single individual.  A duumvirate, as originally defined, referred to the offices of the various duumviri (of two) under the Roman Republic and while there were later triumvirates (of three) and beyond, it was usually the Roman practice to use duumvirate in the sense of “rule by more than one”.

A classical duumvirate is obviously still possible but while instances of genuine co-rule are rare, the shared model has proved a useful tactic in states where the lines of geographic definition don’t align with tribal, religious or ethnic identity.  There, presidencies can be shared, sometimes on a sequential basis (which is another expression of co-rule) but also simultaneously, an illustrative example of which is the office of the Presidency of Bosnia and Herzegovina, a three-member body which collectively serves as head of state of Bosnia and Herzegovina.  Each member elected from a defined region (the Bosniak and Croat members from a joint constituency in the Federation of Bosnia and Herzegovina, the Serb from the Republika Srpska.  The office of the presidency exists as the collective head with one member elected as chairperson which is rotational, changing every eight months; the incumbent thus primus inter pares (first among equals).

Even when an arrangement of two is described as a duumvirate, and may contain some elements of co-rule, it need not of necessity be a system of co-equal rule.  Gough Whitlam (1916-2014; Prime Minister of Australia 1972-1975), always anxious to flaunt his learning before his adoring acolytes, eagerly dug up duumvirate to describe the two man ministry which, for a fortnight, constituted the first Whitlam government but it was merely a device of convenience, the deputy prime-minister (Lance Barnard, 1919-1997, Deputy Prime Minister of Australia 1972-1974) a mere cipher for Whitlam’s initiatives.  The so-called duumvirate actually turned out to be the best days of the Whitlam government; from there it was mostly downhill.  It was a thing made possible only because the results in some seats wouldn’t be known immediately after the 1972 election and thus the names available to be included in the ministry wouldn’t be known for two weeks.  This gave Whitlam the excuse he needed; the Australian Labor Party (ALP) having been in opposition for twenty-three years, he wasn’t prepared to wait.  Thus, Whitlam had the governor-general swear him in as prime minister and Barnard as deputy leader, the two men sharing the twenty-seven portfolios during the fortnight before a full cabinet could be determined.  The “duumvirate” proved a model of administrative efficiency, not something much said of the subsequent cabinet (1972-1975) which, the ALP then in an “egalitarian” phase, insisted should contain all members of the ministry, not the traditional dozen-odd with the others serving in an “outer ministry”.  It was an unwieldy apparatus and the ALP has not subsequently repeated the error; there have been plenty of other mistakes just not that one.

Australia’s tradition of coalition governments has also tempted many to use hyphenated forms to describe administrations although the practice has never been consistent.  The short-lived Reid-McLean ministry (1904-1905) was an example but the moniker was both something of a necessity to distinguish it from the previous Reid ministry in New South Wales (NSW) and a tribute to what sounds one of the more improbable political coalitions: Free traders & protectionists.  Tellingly, it didn’t last long.  There was also the more enduring Bruce-Page government (1923-1929) although it’s only subsequent Country (National) Party leaders who have been inclined to adopt the style.

The constitutional arrangements of a diarchic kingdom are (as in the classic game) reflected in Diarchic Chess, played on the Gustavian board, invented by Gustav III of Sweden (1746–1792; King of Sweden 1771-1792).  The enemy witch has the friendly pieces and pawns under her spell, rendering them unable to attack an enemy king (the bewitchment does not affect the friendly witch and kings).  The only way the spell can be broken is for the friendly witch to sacrifice herself so, when either witch disappears, the spell is broken for all pieces on the board. The witch moves like a rook but can also make one step on the diagonal; princesses move like a bishop and can make one step on the orthogonal; the kings cannot castle; the pawn promotes to queen and other pieces, but not to witch.  The goal remains checkmate.

The kings being immune from attack (except by the witch), they are powerful attacking pieces and it’s not hard to believe the rules of the game were written by a king on his throne.  However, the game would suit not all kings because to take advantage of the rules, a king must be both (1) aggressive early in the game and (2) maintain a position cognizant the enemy witch may sacrifice herself, making the king suddenly vulnerable to the enemy pieces.  King Gustav never indicated if he'd enjoyed some experience of self-sacrificing witches or if the rule was just an imaginative flourish but it is a vital aspect of Diarchic Chess, in one move perhaps transforming the contest.  In practice, it’s a radically different game.