Axiomatic

Axiomatic (pronounced ak-see-uh-mat-ik)

(1) Of or pertaining to the nature of an axiom.

(2) That which is self-evident or unquestionable; the obvious.

(3) Containing maxims; aphoristic.

(4) In formal logic (or any logical system), as axiomatic system, a set of axioms from which theorems can be derived by the application of by transformation rules.

(5) In mathematics, relating to or containing axioms (now less common).

1797: From the Ancient Greek ἀξιωματικός (axiōmatikós), from ἀξίωμα ((axíōma), genitive axiomatos) (a self-evident principle), the construct being axiōmat (stem of axíōma) + the suffix ikos (and the related ic).  The now less common form axiomatical was known as early as the 1580s.  The ikos suffix was from κός (kós) with an added i, from i-stems such as φυσι-κός (phusi-kós) (natural), through the same process by which ῑ́της (ī́tēs) developed from της (tēs), occurring in some original case and later used freely.  It was cognate with the Latin icus and the Proto-Germanic igaz, from which came Old English iġ (which in Modern English ultimately was resolved as y), the Old High German ig and the Gothic eigs.  The ic suffix forms adjectives from other parts of speech.  It occurred originally in Greek and Latin loanwords (metallic; poetic; archaic; public etc) and, on this model, was used as an adjective-forming suffix with the particular sense of “having some characteristics of”, as opposed to the simple attributive use of the base noun (balletic; sophomoric etc), “in the style of” (Byronic; Miltonic etc), or “pertaining to a family of peoples or languages” (Finnic; Semitic; Turkic).  The -ic suffix was from the Middle English -ik, from the Old French -ique, from the Latin -icus, from the primitive Indo-European -kos & -ḱos, formed with the i-stem suffix -i- and the adjectival suffix -kos & -ḱos.  The form existed also in the Ancient Greek as -ικός (-ikós), in Sanskrit as -इक (-ika) and the Old Church Slavonic as -ъкъ (-ŭkŭ); A doublet of -y.  In European languages, adding -kos to noun stems carried the meaning "characteristic of, like, typical, pertaining to" while on adjectival stems it acted emphatically; in English it's always been used to form adjectives from nouns with the meaning “of or pertaining to”.  A precise technical use exists in physical chemistry where it's used to denote certain chemical compounds in which a specified chemical element has a higher oxidation number than in the equivalent compound whose name ends in the suffix -ous; (eg sulphuric acid (H₂SO₄) has more oxygen atoms per molecule than sulphurous acid (H₂SO₃).  Axiomatic & axiomatical are adjectives, axiomatize & axiomatize are verbs and axiomatically is an adverb.  Clumsy forms (sometimes hyphenated) like nonaxiomatic & unaxiomatic are created as required.

In mathematics (notably in including geometry, algebra, and set theory), an axiomatic system (“deductive system” or “formal system” seem to be the more fashionable terms) is a set of axioms or postulates, which, coupled with rules of inference, can be used to derive theorems or statements from those axioms.  In mathematics, there are collections of equations which can be used to document the processes but in any form of applied logic these systems provide a rigorous foundation for reasoning and proof, using what can be reduced to a mathematical process.  In axiomatic systems, axioms are assumed to be true without proof and the rules of inference are used to derive new statements from the axioms; theorems derived from the axioms are then considered to be true, based on the validity of the axioms and the rules of inference.

Axiomatic: If crooked Hillary Clinton is using a cell phone, she will be deleting something.

In the discipline of philosophy, even those parts which are not inherently mathematical (such as formal logic), the axiomatic system works in a similar way in that a statement, proposition, or principle that is considered self-evident or universally accepted without needing to be proven.  Axioms are thus often used as the starting point for logical reasoning or the foundation upon which a system of thought or theory is built, assumed to be true and are not subject to further analysis or questioning within the context of the system they are part of.  There are a number of highly technical rules which define whether a axiomatic system can be described as “consistent” but that means that within its own terms it contains nothing contradictory.  In other words, from the elements of any axiomatic system, it’s not possible to be either proven or disproven. This differs from one labeled “independent” in that that status is defined by them not being proven or disproven from other axioms in the system.  An axiomatic system is labeled “complete” if for every statement, either itself or its negation is derivable from the system's axioms (implicit in which is that every statement is capable of being proven true or false).

Not axiomatic: The real Lindsay Lohan and Take Two Interactive’s alleged doppelganger in Grand Theft Auto V (GTA5).

Lawyers too like the word “axiomatic”, possibly because concepts like “foreseeability” and “causation” are such an essential part of their training.  The use though exists within different parameters to that of mathematics.  In Lindsay Lohan vs Take Two Interactive Software Inc et al (APL-2017—00027 and APL-2017-00028 (November 2017)), the New York Court of Appeals held that a certain section of an act “categorically excludes works of fiction, a protected category of expression beyond the narrow scope of the statutory phrases advertising and trade”, noting the US Supreme Court (USSC) had “reversed course to recognize First Amendment protections for fiction”.  The Court of Appeal explained that after the USSC “limited Section 51 claims for fictionalization” to factual works that place persons in a false light, subsequent case law both isolated the commercial interest protected by the right of publicity and recognized “the right of publicity does not attach” where “it is evident to the public that the events so depicted are fictitious.”  The judgment noted with approval the decision of the California Supreme Court which “famously” recognized fiction writers may “more persuasively be able to more accurately express themselves by weaving into the tale persons or events familiar to their readers”, adding “correctly”, that “the choice is theirs”.  “This categorical protection is now axiomatic”.  Once can see what the judges meant and of course they were correct but what can be held to be “axiomatic” in law can differ from the same thing in mathematics because in the world of numbers, there is no superior court able to rule 2+2=5.  Their position is more akin to the philosophers who for centuries until 1697 could regard as inviolate the axiom to “all swans are white and all non-white birds are not swans”.

Canon

Canon (pronounced kan-uhn)

(1) An ecclesiastical rule or law enacted by a council or other competent authority and, in the Roman Catholic Church, approved by the pope; the body of ecclesiastical law.

(2) In certain denominations in Christianity, one of a body of dignitaries or prebendaries attached to a cathedral or a collegiate church; a member of the chapter of a cathedral or a collegiate church.

(3) In the Roman Catholic Church, one of the members (canons regular) of certain religious orders.  Historically, a member of either the Augustinian or Premonstratensian, living communally as monks but performing clerical duties.

(4) The body of rules, principles, or standards accepted as axiomatic and universally binding in a field of study or art.

(5) A fundamental principle or general rule.

(6) A standard; criterion.

(7) The books of the Bible recognized by any Christian church as genuine and inspired.

(8) Any officially recognized set of sacred books.

(9) A piece of music in which an extended melody in one part is imitated successively in one or more other parts (fugal).

(10) A size of printer's type (historically used for the printing of church canons), equal to 48 point (archaic).

(11) In hymnography, a kind of hymn in Eastern Orthodox Christianity

(12) In bell-founding, one or more hanging loops cast integrally with the crown.

(13) In Roman law, a rent or stipend payable at some regular time, usually annually).

(14) In cooking, the alternative spelling of cannon (rolled and filleted loin of meat).

1150-1200: In ecclesiastical use, from the Middle English canonicus (shared with French), a back formation from the Old English canōnic (one under rule), from the Medieval Latin canōnicus (of or under rule).  The word in Ancient Greek was kanōnikós from kanon (any straight rod or bar; rule; standard of excellence), possibly from kanna (reed).  As applied to the clergy, the title dates from circa 1200, from the Anglo-French canun, from the Old North French canonie (which is Modern French is chanoine), from the Church Latin canonicus (clergyman living under a rule), the noun use of the Latin adjective canonicus (according to rule).  The meaning “standard, accepted list” is from the Old English, again from the Latin, from the Greek kanōn (rule, rod for measuring, standard), related to kanna (a reed or cane) and in English, dates from circa 1400 but only in the context of the lists assembled for ecclesiastical purposes.  Canon is a noun & adjective, canonization is a noun, canonize is a verb, canonized is a verb & adjective and canonical is an adjective; the noun plural is canons.

The Latin word was taken in ecclesiastical use for "decree of the Church" and eventually this expanded into the codified "Canon Law" of the Church.  The general sense of "a rule or principle" dates from the late fourteenth century while the idea of a "standard of judging" is from circa 1600.  From circa 1400 as "The Scriptures", the word was applied to those books of the Bible accepted by the Christian church" and this later extended to secular books of admitted excellence or supremacy (an most importantly meeting the approval of the Church) and in some archives there are a number of such lists but according to Harold Bloom (1930-2019) who noted the history in The Western Canon (1994), the "...secular canon, with the word meaning a catalog of approved authors, does not actually come into use until the mid-eighteenth century."

Thou shalt not.

The canon as a "catalogue of acknowledged saints" is from 1727, reflecting the implications of the late fourteenth century verb canonize and the companion noun canonization.  To canonize was to "place officially in the canon or calendar of saints" and was from the Old French canonisier and directly from the Medieval Latin canonizare, from the Late Latin canon (church rule, catalogue of saints).  The noun canonization (act of enrolling a beatified person among the saints) was from the Medieval Latin canonizationem (nominative canonizatio), the noun of action from the past-participle stem of canonizare.  Use has varied greatly between pontificates, something explained by the power to canonize lying exclusively in the gift the pope since 1179.  The related forms are canonized, canonizing and the marvelous canonicity.  The use in music to describe "a kind of fugal composition" is from the 1590s.  In the traditional sense of the Western canon of literature, although never a fixed-set, it’s become increasingly contested, even to the point of being criticized, inter alia, by post-modernists, critical theorists, Marxists and feminists as a form of cultural imperialism.  

Lindsay Lohan's canon of film

1998 The Parent Trap

2003 Freaky Friday

2004 Confessions of a Teenage Drama Queen

2004 Mean Girls

2005 Herbie: Fully Loaded

2005 My Scene Goes Hollywood: The Movie

2006 A Prairie Home Companion

2006 Just My Luck

2006 Bobby

2006 Friendly Fire

2006 The Holiday

2007 Chapter 27

2007 Georgia Rule

2007 I Know Who Killed Me

2009 Labor Pains

2010 Machete

2011 Lindsay Lohan

2012 First Point

2013 Inappropriate Comedy

2013 Scary Movie 5

2013 The Canyons

2015 Till Human Voices Wake Us

2019 Among the Shadows (The Shadow Within in some markets)

2022 Falling for Christmas

2023 Irish Wish

2024 Our Little Secret

2025 Freakier Friday

Pope Leo’s canon of film

Coinciding with having summonsed to the Vatican a goodly number of film stars, directors, producers and such, the Holy See’s press office released the names of Leo XIV’s (b 1955; pope since 2025) four favourite movies, the pontiff himself confirming the list during an interview with Variety.

It's a Wonderful Life (1946)
The Sound of Music (1965)
Ordinary People (1980)
La Vita è Bella (Life is Beautiful (1997))

The Hollywood actors and filmmakers who enjoyed a papal audience would have learned His Holiness values movies not only for their intrinsic qualities but also for their social role, lamenting the diminishing number of neighborhood cinemas meant many no longer enjoyed the shared experience of communal viewing.  The pope’s message was the film industry was a “workshop of hope” and a vital institution during a time of global instability and “digital overload”; while the celebrities doubtlessly enjoyed the photo-opportunity and listened politely, whether the suggestion they should “…confront violence, war, poverty and loneliness” and will “…cooperate in affirming the social and cultural value of this activity” remains to be seen.

Conclusion to be drawn from His Holiness's canon of film: He wouldn’t have been much fun at parties but will go to Heaven.

A romantic nihilist's canon of film

1939 Wuthering Heights

1958 Touch of Evil

1958 Vertigo

1964 Dr Strangelove

1970 Zabriskie Point

1971 A Clockwork Orange

1971 Dirty Harry

1973 The Exorcist

1979 Nosferatu the Vampyre

1986 The Texas Chainsaw Massacre 2

1987 Nightmare on Elm Street III

1987 Withnail and I

1990 Truly, Madly, Deeply

1991 Europa (Zentropa in the US)

1991 Delicatessen

Conclusion to be drawn from a romantic nihilist’s canon of film: Will go straight to Hell.

Club

Club (pronounced kluhb)

(1) A heavy stick, usually thicker at one end than at the other, suitable for use as a weapon; a cudgel.

(2) A group of persons organized for a social, literary, athletic, political, or other purpose.

(3) The building or rooms occupied by such a group.

(4) An organization that offers its subscribers certain benefits, as discounts, bonuses, or interest, in return for regular purchases or payments.

(5) In sport, a stick or bat used to drive a ball in various games, as golf.

(6) A nightclub, especially one in which people dance to popular music, drink, and socialize.

(7) A black trefoil-shaped figure on a playing card.

(8) To beat with or as with a club.

(9) To gather or form into a club-like mass.

(10) To contribute as one's share toward a joint expense; make up by joint contribution (often followed by up or together).

(11) To defray by proportional shares.

(12) To combine or join together, as for a common purpose.

(13) In nautical, use, to drift in a current with an anchor, usually rigged with a spring, dragging or dangling to reduce speed.

(14) In casual military use, in the maneuvering of troops, blunders in command whereby troops get into a position from which they cannot extricate themselves by ordinary tactics.

(15) In zoological anatomy, a body part near the tail of some dinosaurs and mammals.

(16) In mathematical logic and set theory, a subset of a limit ordinal which is closed under the order topology, and is unbounded relative to the limit ordinal.

(17) In axiomatic set theory, a set of combinatorial principles that are a weaker version of the corresponding diamond principle.

(18) A birth defect where one or both feet are rotated inwards and downward.  Dr Joseph Goebbels (1897-1945; Nazi propaganda minister 1933-1945) was born with the condition although in early self-propaganda he did attempt to suggest it was a battlefield injury from World War I (1914-1918); Goebbels never served in the military.  

1175-1225: From the Middle English clubbe, derived from the Old Norse klubba (club or cudgel) akin to clump, from Old English clympre (lump of metal) related to the Middle High German klumpe (group of trees).  The Proto-Germanic klumbon was also related to clump.  Old English words for this were sagol and cycgel.  The Danish klőver and Dutch klaver (a club at cards) is literally "a clover."  Ultimate root is the classical Latin globus or glomus (forming into a globe or ball), a later influence the Middle Low German kolve (bulb) and German Kolben (butt, bulb, club).  The sense of a "bat used in games" is from mid-fifteenth century; the club suit in the deck of cards is from the 1560s although the pattern adopted on English cards is the French trefoil.  The social club emerged in the 1660s, apparently an organic evolution from the verbal sense "gather in a club-like mass", first noted in the 1620s, then, as a noun, the "association of people", dating from the 1640s.  The Club Sandwich was probably first offered in 1899, the unrelated club soda in 1877, originally as the proprietary name Club Soda.  Club, clubbishness & clubbing are nouns & verbs, clubber is a noun, clubbed is a verb & adjective, clubby & clubbish are adjectives and clubbily is an adverb; the noun plural is clubs.

On her Only Fans page, Tash Peterson shows her club membership.

Something of a local legend in the world of vegan activism, Tash Peterson (b circa 1995) is an animal rights activist based in Perth, Australia.  Not part of the the militant extreme of the movement which engages in actual physical attacks on the personnel, plant & equipment of the industries associated with animal slaughter, Ms Peterson's form of direct action is the set-piece event, staged to produce images and video with cross-platform (Instagram, TikTok etc) appeal, the footage she posts on social media freely available for re-distribution by the legacy media, her Instagram feed providing a sample of her work in various contexts.  The accessories used include blood (reputedly from slaughterhouses) and very fetching figure-fitting costumes styled to resemble various animals including cows, her favored locations including the meat section of supermarkets, cafés and restaurants serving animal flesh, processing facilities associated with the slaughter industry and any events celebrating the carnivorous.  Ms Peterson's other club membership is that of the vegansexuals (vegans who choose to have sex or pursue sexual relationships only with other vegans).  Vegansexuals differ from vegesexuals in that while vegetarians exclude from their diet meat, poultry, and fish, many do consume dairy, eggs and honey, all products Ms Peterson says involve animal cruelty or exploitation and according to her, "plant-powered penises last longer".  Based presumably on her empirical findings, that knowledge is a helpful contribution to civilization. 

The Club Sandwich

Most historians of food suggest the club sandwich (in the sense of an item able to be ordered) first appeared on a menu in 1899 at the Union Club of New York City.  It was however made with two toasted slices of bread with a layer of turkey or chicken and ham between them, served warm, not the three slices with which it’s now associated; at that point the "club" was merely self referential of the institution at which it was served.  Others suggest it originated in 1894 at an exclusive gambling club in New York’s Saratoga Springs; the former is more accepted because there’s documentary evidence while the latter claim is based on references in secondary sources.  It’s a mere etymological point; as a recipe, what’s now thought of as a club sandwich had doubtless been eaten for decades or centuries before the words Club Sandwich appeared on a menu.  The notion that club is actually an acronym for "chicken and lettuce under bacon" appears to be a modern pop-culture invention, derived from a British TV sitcom, Peter Kay’s (b 1973) Car Share (episode 5: Unscripted, 7 May 2018) in what’s claimed to be an un-scripted take, although, on television, very little is really ad-lib and within the industry, "reality" has a specific, technical meaning.  On the show, the discussion was about the difference between a BLT (bacon, lettuce & tomato) and a club sandwich.  On the internet the factoid went viral but was fake news.

Seemingly sceptical: Lindsay Lohan contemplates club.

Ingredients

12 slices wholegrain or rye bread

12 rashers rindless, shortcut, peach-fed bacon

Extra-virgin olive oil

2 free-range eggs

½ cup whole egg mayonnaise

12 cos lettuce leaves

320g sliced lean turkey breast

4 ripe Paul Robeson heirloom tomatoes, sliced

A little freshly-chopped tarragon

Ground smoked sea salt & freshly cracked black peppercorns

Instructions

(1) Preheat a grill tray on medium.  Place half the bread under grill and cook until lightly toasted.  Repeat with remaining bread.

(2) Lightly brush both sides of bacon with oil.  Place under grill and cook for 2-4 minutes each side according to taste.  Once removed, place on a paper towel, turning over after one minute.

(3) Fry eggs, preferably leaving yokes soft and runny.  Fold tarragon into mayonnaise according to taste.   

(4) Spread 8 of the slices of toast with mayonnaise.  Arrange half of the lettuce, turkey and tomatoes over 4 slices.  Evenly distribute the fried eggs.

(5) Top with a second slice of toast with mayonnaise. Then, add remaining lettuce, bacon and tomato. Season well with salt and pepper. Top with remaining pieces of toast.

(6) Cut each sandwich in half or quarters according to preference, using toothpicks driven through centre to secure construction.

Variations

Chefs are a dictatorial lot and tend to insist a club sandwich must be a balanced construction with no predominant or overwhelming taste or texture; with chefs, the trick is to agree with everything they say and then make things to suit individual taste.  By varying the percentages of the ingredients, one can create things like a bacon club with extras and vegetarian creations are rendered by swapping bacon and turkey for aubergine and avocado.  A surprising number find tomato a mismatch, some add cheese or onion while many prefer butter to mayonnaise.  In commercial operations like cafés, tradition is to serve clubs with French fries but many now offer salads, often with a light vinaigrette dressing.  Served with soup, it’s a meal.

1946 Lincoln Club Coupe (body style 77).  When production of the V12 Lincoln Zephyr (1936-1942) resumed in 1946, the cars were sold simply as Lincolns with no model designation, differentiated by the style of coach-work (Sedan, Club Coupe & Convertible Coupe).  When production ended in 1948, it was the last of the American V12s.

The mysterious term “club coupe” emerged in the 1930s to distinguish the style from the “business coupe”, the latter a two door car with only a front seat, the rear compartment used to augment the space in the trunk (boot), the target market the numerous “travelling salesmen” who needed a vehicle with lots of secure storage for their wares.  What the term “club coupe” described was a two-door car with a rear passenger including a bench seat for two or three.  The use of the word “club” was an example of “aspirational branding”, a marketing flourish intended to suggest something more upscale than the utilitarian business coupe, the invocation that of the style and exclusivity of the “private club”.  Being a product of the marketing department, “club coupe” was never precisely defined and while the characteristics associated with the style were sometimes identifiable, never were they long consistent.

1951 Ford Custom Deluxe Club Coupe; long model names are nothing new.

The mid-century tendency was to use a body shorter than that of a sedan but retaining the convenience of a full-size back seat (unlike the single-seat business coupe) but as the “two door sedan” emerged as a descriptor things became fuzzy and by the time the two door hardtops appeared at scale in the 1950s, it wasn’t surprising “club coupe” fell from favour.  Ford in 1954 offered a club coupe but they were the next season renamed “Tudor sedan” (ie a two-door sedan) but made the use murkier still by calling the Customline Six two-door a "Tudor Sedan" and the new V8 Fairlane a “Club Sedan”; business coupes and club sedans lingering for years in the line-up but the club coupe vanished until 1966.  The 1960s revival was a use of the word to allude to the upmarket fittings once associated with the more luxurious club coupes of the pre-war years and like “landau”, “brougham” and such, was just another model designation, suggestive of some link to a happier past.

Promotional images used for 2015 Holden Commodore Clubsport R8 25^th Anniversary Edition.  Note the bogan-themed tyre marks; Holden knew their target-market.

The meaning denoted was different in 1990 when Holden added the V8 HSV (Holden Special Vehicles) Clubsport to the VN range as a “de-contented” entry-level model, along the lines of the original Plymouth Road Runner (1968-1970), the message being: fewer fittings meant lower cost, reduced weight and thus higher performance.  In this case the “club” element of the name denoted a vehicle suitable for amateur motor sport (ie “club-level” competition) in that the car could be road-registered and driven to racetracks where it could be used in standard form or with only slight, temporary modifications (tyres, brake-pads, exhaust systems etc). The Clubsport would remain in the line-up until the end of Holden production in 2017 although, for various reasons, equipment levels steadily increased.

Joyous German Porsche fanboys at a club meeting in 1957, held for them to meet Ferdinand Anton Ernst "Ferry" Porsche (1909–1998), a event they would have found a quasi-religious experience similar to that felt by Apple cultists permitted to be in the same room as Steve Jobs (1955–2011).

It was in the US in the 1930s that manufacturers began to dub cars “club this, that or the other” in a (vague) allusion to the up-market “private club”.  In Germany at the time, “club” was understood as “a stout stick with which one may strike another” and for some years cudgels had been the language of political discourse as the Communists and Nazis battled for control of the streets.  The Nazis clubs prevailed and under the Third Reich (1933-1945) private societies and associations became rare as the party and state attempted to assume totalitarian control, the party deluding itself into believing its crackdown on independence of thought had solved the “Freemason problem”, even creating a “Freemason Museum” on Berlin’s Prinz-Albrecht-Palais (conveniently close to Gestapo headquarters) to exhibit relics of the “vanished cult”.

Founding articles of the Westfälischer Porsche Club Hohensyburg.

After World War II (1939-1945) the private societies returned (including the scourge of Freemasonry) and on 26 May, 1952, seven fanboys (soon there were 13) of the Porsche sports cars (in production since 1948) formed the Westfälischer Porsche Club Hohensyburg; as Porsche Club Westfalen e.V. the club still exists and is based in Dortmund.  It was the world’s first “Porsche club” of which there are now hundreds in a reputed 86 countries with a membership roll believed to be close to a quarter-million and although there are factions devoted to other models, the core of the cult is a kind of “freemasonry of the 911”, a car with a lineage in which traces of the 1948 models remain detectable.  The club’s name also honored the Hohensyburg racecourse near Dortmund, which locals liked to call the “Westfalens Nürburgring” (Nürburgring of Westphalia).

2012 Porsche 911 Club Coupé in Familiengrün.

Although “fanboy” is understood to mean something like übertriebener Fan (excessively obsessive fan), blinder Anhänger (blind follower) or fanatischer Anhänger (fanatical follower), German has absorbed the English slang “fanboy” and uses it unmodified.  In 2012, Porsche celebrated the company’s 60^th anniversary and one component in the celebrations was a run of 13 911 Club Coupés, the unusual production volume a tribute to those 13 fanboys of 1952 who were the foundation members of world’s first “Porsche Club”.  Based on the 991 series (2011-2019) 911 (the concept in series production since 1964), the Club Coupé was bundled with the Sport Design package, X51 Powerkit, body-colored Sport Techno wheels, PCCB (Porsche Ceramic Composite Brakes which used a ceramic disc-rotor reinforced with carbon fibre), Club-themed door sills, and PASM (Porsche Active Suspension Management).

1969 Porsche 911S (chassis #: 911 0300014) in olive green metallic, once the personal car of Ferry Porsche.

Although the specification was standard, Ferry Porsche got a sort of “advance copy” of the new model because it was one of fourteen built (chassis #: 911 0300013 skipped for “superstitious reasons”) for internal use before the summer holidays so customers had to wait a while to enjoy the 180 HP extracted from the 2.2 litre (134 cubic inch) flat-six for the new 911S.  Others in the batch (01, 02 & 03) were allocated to the competition department for use in the 1969 Acropolis Rally which a 911S won.  What the 911 cultists adore is little details the factory added or omitted and of note are the missing front over-riders (an aesthetic choice by Ferry Porsche), a fuel-injection system from the 1966 906 (Carrera 6) and even a tow bar; the provenance of the latter two is uncertain but the tow-bar is a genuine factory part.  One marker of the uniqueness of the run in 2012 of the 13 Club Coupés was the color; although the factory listed the hue as Brewstergrün (Brewster Green), it was known internally as Familiengrün (Family Green), used for Wolfgang Porsche’s (b 1943) personal 911s.  Familiengrün is a concept rather than a chemical specification the influences over the years have included Oakgreenmetallic, Olivegreen and Emeraldgreenmetallic.

Asymptote

Asymptote (pronounced as-im-toht)

(1) In mathematics, a straight line which a curve approaches arbitrarily closely as it extends to infinity; the limit of the curve; its tangent “at an imaginary representation of infinity”.

(2) By extension, figuratively, that which comes near to but never meets something else (used in philosophy, politics, conflict resolution etc).

1650–1660: From the Greek asýmptōtos (not falling together).  The Ancient Greek ἀσύμπτωτη (asúmptōtē) was the feminine of Apollonius Pergaeus' Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos (Apollonius of Perga (Apollonius Pergaeus (circa 240-190 BC)), an astronomer whose most noted contribution to mathematics were his equations exploring quadratic curves.  The construct of the Ancient Greek adjective ἀσύμπτωτος (asúmptōtos) (not falling together) was a- (not) + sýmptōtos (falling together (the construct being +‎ συν (-sym-) (together) + πτωτός (ptōtós) (falling; fallen inclined to fall), the construct being ptō- (a variant stem of píptein (to fall) (from the primitive Indo-European root pet (to rush; to fly)) + -tos (the verbid suffix).  The adjective asymptotic (having the characteristics of an asymptote) dates only from the 1970s.  Asymptote is a noun & verb, asymptotia & asymptoter are nouns, asymptotic & asymptotical are adjectives, asymptoted & asymptoting are verbs and asymptotically is an adverb; the noun plural is asymptotes.

Lines, curves & infinity

The noun asymptote describes a straight line continually approaching but never meeting a curve, even if extending to infinity.  This means that although the distance between line and curve may tend towards zero, it can never reach that point, which is hard to visualize but explained by the notion of the line only ever able to move half the distance required to achieve intersection.  At some point such a thing becomes impossible usefully to represent graphically and even exactly to define the asymptotic using integer mathematics would be unmanageable, thus the use of the infinity symbol (∞).

Horizontal (left), vertical (centre) and oblique asymptotes (right).

There are (1) horizontal asymptotes (as x goes to infinity (in either direction (ie also negative (-) infinity)), the curve approaches b which has a constant value), (2) vertical asymptotes (as x (from any direction) approaches c (which has a constant value), the curve proceeds towards infinity (or -infinity) and (3) oblique asymptotes (as x proceeds towards infinity (or -infinity), the curve goes towards a line y=mx+b (m is not 0 as that is a horizontal asymptote).

The logarithmic spiral and the asymptote.

Although usually depicted on a flat plane, a curve may intersect the asymptote an infinite amount of times.  A spiral with a radius is a logarithmic spiral, distinguished by the property of the angle between the tangent and the radius vector being constant (hence the more popular names “equiangular spiral” or “growth spiral”, the latter favored by laissez faire economists.  The shape appears often in the natural environment in objects and phenomenon as otherwise dissimilar as sea-shells, hurricanes and galaxies near (in cosmic terms) and far.  This diagram was posted on X (formerly known as Twitter) by Dr Cliff Pickover (@pickover) who writes the most elegant explanations which help draw the eye to the often otherwise hidden beauty of mathematics.

Zeno of Elea (Ζήνων ὁ Ἐλεᾱ́της (circa  490–430 BC)) was a Greek philosopher of the Eleatic school, an ever-shifting aggregation of pre-Socratic thinkers based in the lands around the old colony of Ἐλέα (Elea, in the present day southern Italian region of Campania, then called Magna Graecia).  Among his surviving thoughts were nine musings (now called Zeno's paradoxes) on the nature of reality, the details of which survived only in the writings of others which has led to some speculation perhaps not all came originally from the quill of Zeno.  Although most of the paradoxes revolve around the notion movement is illusory (and thus effortlessly & instantly resolved by every student in their first Philosophy 101 lecture), they are all less about physics than language and mathematics, the most intriguing of them one of the underlying structures of the argument about whether “now” does or can exist, the “ultras” of one faction asserting “now cannot exist” the other that “only now can exist”.  In that spirit, there’s much to suggest Zeno was aware of the absurdity of many of “his” paradoxes and created them as (1) tools of intellectual training for his students and (2) devices to illustrate how ridiculous can be the result if abstraction is pursued far beyond the possibilities of reality (ie not all arguments pursued to their “logical conclusion” produce a “logical” result).  One of Zeno’s paradoxes contains an explanation of why a curve might never reach a straight line, even if that line stretches to infinity: If the curve can at any time move closer to the line only by half the distance required to intersect, then the curve can only ever tend towards the line.  The two will never touch.

Christian von Wolff (circa 1740), mezzotint by Johann Jacob Haid (1704-1767).

The German philosopher Baron Christian von Wolff (1679-1754) was an author whose writings cover an extraordinary range in formal philosophy, metaphysics, ethics and mathematics and were it not for the way in which Immanuel Kant’s (1724-1804) work has tended to be an intellectual steamroller flattening the history of German Enlightenment rationality, he probably now be better remembered beyond the profession.

What most historians agree is the paradoxes were written to provide some framework supporting Parmenides' (Parmenides of Elea (Παρμενίδης ὁ Ἐλεάτης (circa 515-570 BC)) was a teacher of the younger Zeno) doctrine of monism (that all that exists is one and cannot be changed, separable only descriptively for purposes of explanation).  The word “monism” was coined by Christian von Wolff and first used in English in 1862; it was from the New Latin monismus, from the Ancient Greek μόνος (mónos) (alone).  Spending years contemplating things like monism may be one of the reasons why so many German philosophers went mad.  So the doctrine of monism is one of the oneness and unity of reality, despite the appearance of what seems a most diverse universe.  That “one-thingism” (that one of philosophy’s great contributions to language) attracted political thinkers along the spectrum but most appealed to those who hold there must be a single source of political authority, expressed frequently as the need for the church to be subordinate to the state or vice versa although the differences may be less apparent than defined: the systems imposed by the ayatollahs in the Islamic Republic of Iran and the Chinese Communist Party (CCP) in the People’s Republic of China structurally more similar than divergent.  Winston Churchill (1875-1965; UK prime-minister 1940-1945 & 1951-1955) once observed that while to political scientists fascism & communism seemed polar opposites, to many living under either the difference may have been something like comparing the North & South Poles, one frozen wilderness much the same as any other.  Arctic geographers would quibble over the details of that but his point was well-understood.

Lindsay Lohan and her lawyer in court, Los Angeles, December 2011.

Because of the self-contained, internal beauty, Monism has attracted long attracted political philosophers with axes to grind.  According to Sir Isaiah Berlin (1909-1997), “value monism” holds there are discoverable, axiomatic ethical principles from which all ethical knowledge may be derived, that ethical reasoning is algorithmic and mechanical, and that it seeks permanent, “final solutions” (no historical baggage in the phrase) to all ethical conflicts.  Berlin had his agenda and that was to warn monism tends to support political despotism, rejecting Immanuel Kant’s (1724–1804) argument “asymptotic monism” is not merely compatible with liberty and liberal toleration but actually a prerequisite for these values.  Although the phrase “Kant’s asymptotic monism” appears often, the phrase was never in his writings and is an encapsulation used by later philosophers to describe positions identifiably Kantesque.  His own philosophy has often been called “a form of transcendental idealism” which holds that the mind plays an active role in shaping our experience of the world, one’s individual’s experience of things not a direct reflection of what is but a construct shaped by the categories and concepts one’s minds impose on one’s experience.  Implicit in Kant is there is certainly one, ultimate, objective reality but experience of reality is limited and shaped by one’s cognitive capacities: because one’s experience of reality is always incomplete and imperfect, it can only ever approach a complete understanding of reality.  One’s cognitive capacities might improve but can only ever tend toward and never attain perfection.  Reality is the asymptote, one’s cognitive capacity the curve.