Delta

Delta (pronounced del-tuh)

(1) The fourth letter of the Modern Greek alphabet (Δ, δ).

(2) The consonant sound represented by this letter.

(3) The fourth in a series of items.

(4) Anything triangular, an allusion to the Greek capital delta (Δ).

(5) In mathematics, an incremental change in a variable, as Δ or δ.

(6) A nearly flat plain of alluvial deposit between diverging branches of the mouth of a river, often, though not necessarily, triangular.

(7) A word used in communications to represent the letter D (usually initial capital letter); Used in the ICAO (International Civil Aviation Organization) radiotelephony spelling alphabet (usually known as the NATO phonetic alphabet).

(8) In astronomy, a star that is usually the fourth brightest of a constellation (initial capital letter).

(9) In computing, a small but noticeable effect or the set of differences between two versions of a file; in informal use, a small but noticeable effect.

(10) In surveying, the angle subtended at the centre of a circular arc.

(11) A type of cargo bike that has one wheel in front and two in back.

(12) In electrical engineering (often attributive), the closed figure produced by connecting three coils or circuits successively, end for end, especially in a three-phase system.

(13) In finance, the rate of change in an option value with respect to the underlying asset's price.

(14) In chemistry, a value in delta notation indicating the relative abundances of isotopes or relating to or characterizing a polypeptide chain that is one of five types of heavy chains present in immunoglobins.

(15) In aerodynamics, a type of wing.

(16) The NATO code name for a class of Soviet nuclear-powered ballistic missile submarine armed with sixteen multi-warhead missiles.

(17) In physics, of or characterizing the atom or radical group that is fourth in position from the functional group of atoms in an organic molecule.

(18) In US Space Force use, a unit, nominally headed by a colonel, equivalent to a USAF operations wing, or an army regiment.

(19)   In electrical engineering, the closed figure produced by connecting three coils or circuits successively, end for end, especially in a three-phase system.

Circa 1200: From the Middle English deltha from the Latin delta from the Ancient Greek δέλτα (délta), from the Phoenician dalet & daleth (tent door).  It was akin to the Hebrew dāleth.  It was the fourth letter of the Greek alphabet (equivalent to the Modern English D) and was shaped like a triangle (Δ).  The sense of a delta being a "triangular island or alluvial tract between the diverging branches of the mouth of a great river" is because the Ancient Greek writer Herodotus (circa 484–circa 425 BC) used it to describe the mouth of the Nile River (now known as the Nile Delta).  That was picked up in English during the 1550s and applied to other river mouths (often of quite different shapes) by 1790.  The related forms are deltaic and deltification.  In pre-modern medicine, the deltoid muscle (the large muscle of the shoulder; triangular, resembling the Greek letter delta) was described in 1758, the name from the Ancient Greek deltoeides (triangular, literally "shaped like the letter delta).  In modern use, the "deltoid muscle" gained the short-form “delts” in 1977.  The related form is deltoidal.

The delta-wing

Gloster Javelin (1951-1967).  The first twin-engined delta-wing in service, the Javelin was the UK’s long-term solution to its need for an all-weather interceptor, the post-war technology gap until then filled by the stop-gap Gloster Meteor and that most improbable cold-war fighter, the de Havilland Mosquito.  The Javelin was the last aircraft to bear the Gloster name, the company absorbed into the morass created by the mergers, acquisitions and nationalization that befell British industry between Attlee and Thatcher. 

In aviation, the delta shape pre-dated aircraft by centuries, triangular stabilizing fins for rockets described in the sixteenth and seventeenth centuries and the first lifting wing in delta form patented in 1867 for use by a dart-shaped, rocket-propelled airplane.  However, although there were prototypes and much theoretical work was done during the first half of the twentieth century, it wasn’t until the late-1940s when jet propulsion made possible high-speed subsonic and supersonic flight that it was possible to build airframes which could take advantages of the delta-wing’s unique properties.

Lockheed SR-71 Blackbird (1963-1999).  A product of Lockheed’s Skunk Works, although in development as a high-altitude interceptor since 1959, the US government didn’t admit the SR-71 existed until 1964 and decided ultimately to use it for reconnaissance and research into supersonic flight.  The SR-71 in 1976 set the world record for the fastest flight by an air-breathing manned aircraft and the mark still stands.

The delta form offers structural advantages and aerodynamic characteristics suited to the fluid dynamics of airflow in supersonic conditions.  To suit different applications, design variations have evolved, with and without additional stabilizing surfaces.  The long root chord of the delta wing and minimal structure outboard is inherently structurally efficient, able to be built stronger and stiffer yet lighter than a swept wing of equivalent lifting capability.  It’s thus simple and relatively inexpensive to build.

Avro Vulcan (1956-1984).

Until the UK adopted the submarine-launched Polaris missile system, the Vulcan was the platform for the UK’s independent nuclear deterrent and it remained in service long enough to be deployed for its only combat mission, a flight of five aircraft used for (conventional bombing) missions during the 1982 Falklands War.  Each aircraft flew almost 4000 miles  (6,500 km) from Ascension Island, Victor tankers used for the air-to-air refueling, almost 1.1 million gallons (5 million litres ) of fuel burned each mission.

The long root chord also allows a deeper structure for a given aerofoil section, providing more internal volume for fuel and other storage without a significant increase in drag although, on supersonic designs, designers often take the opportunity to use a thinner aerofoil instead, thereby further reducing drag.  Usefully, the large root chord also provides a large surface area which assists in reducing the minimum speed; a low landing speed being a design objective in most military and civil applications.  Delta wings can be designed to induce vortex lift, so flow separation can be turned into a means of increasing lift and the whole structure is naturally stable in pitch, therefore not requiring a separate tail surface.

Aérospatiale/BAC Concorde (1969-2003).

The Anglo-French supersonic passenger jet operated commercially between 1976-2003.  Flying at twice the speed of sound and carrying up to 128 passengers, it was the longest lasting of its time, the Soviet Tupolev Tu-144 in passenger service only for a few years during the 1970s after which it operated both as a freighter and a research platform and the American SST never progressed beyond engineering mock-ups.  The Americans worked out the economics were never going to make sense; the Soviets had a different relationship to money and the Concorde lasted as long as it did only because the French & British governments wrote-off the development costs.

There are drawbacks.  The large wing area creates more viscous drag for the same amount of lift compared to a high aspect ratio wing; swept wings have a better lift-to-drag ratio than deltas.  Also, high-lift devices like fowler flaps are hard to integrate into delta wings with the rearward location of the trailing edge producing intolerable pitching moments when such flaps would be deflected.  In short, delta wings are superior only in supersonic flight; their best known design probably the Anglo-French Concorde.

Lindsay Lohan in delta skirts.

A delta skirt is characterized by its triangular shape, an allusion to the Greek letter delta (Δ); almost always, a delta skirt is fitted at the waist, flaring out towards the hem, creating the triangular silhouette.  The concept is adaptable and can be made from just about any fabric, the most popular including cotton, taffeta, silk and a variety of other synthetics.  Delta skirts tend to be shorter because to produce the triangular effect as length increases either some sort of internal structure is required or additional material needs to be used, increasing bulk and weight.  Although most associated with younger women, they have been adopted by a number sub-sets from the anime aesthetic, Goths and bohemians to hippies.

Ogee

Ogee (pronounced oh-jee)

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

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

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

(4) In mathematics, an inflection point.

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

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

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

An Ogee arch.

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

An inflection point.

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

The cosmetic surgeon's template.

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

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

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

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

Endurance

Endurance (pronounced en-doo r-uhns or en-dyoo r-uhns)

(1) The fact or power of enduring or bearing pain, hardships, etc.

(2) The ability or strength to continue or last, especially despite fatigue, stress, or other adverse conditions; stamina.

(3) Lasting quality; duration.

(4) Something endured, as a hardship; trial.

1485-1495: From the Middle English enduren from the Old French endurer, from the Classical Latin indūrō (to make hard).  Enduren displaced the pre-900 Old English drēogan (congnate with the Gothic driugan (to serve in arms) which survives dialectally as dree (tedious; dreary)).  The meaning "ability to endure suffering" was first noted in the 1660s. The older forms, enduraunce, indurance, induraunce are all long obsolete.  Construct was endure + ance; the suffix –ance (a process or action) added to the stem of verbs to form a noun indicating a state or condition, such as result or capacity, associated with the verb, this especially prevalent with words borrowed from French.  Many words ending in ance were formed in French by alteration of a noun or adjective ending in ant; ance was derived from the Latin anita and enita.

Endurance Racing

There’s no precise definition of endurance racing, it's just a form of competition of greater duration of length than most.  It’s bounced around over the years but events now regarded as endurance races tend to be over a distance of 625 miles (1000 km) or twelve or twenty-four hours long.  Long races existed from the early days of motorsport, the first twenty-four hour event being on an oval circuit at Dayton, Ohio in 1905, followed soon by the opening event at the purpose-built Brooklands circuit in 1907.  One of the epic races was the Targa Florio, first run in 1906.  Held originally on public roads in the mountains of Sicily near the capital Palermo, it was for decades the oldest event for sports cars and a round of the World Sportscar Championship between 1955-1973.  The first few races were a lap of the whole island but as the volume of traffic and competitors increased, it became too disruptive and the track length was reduced to the 72 kilometre (45 mile) Circuito Piccolo delle Madonie, each Targa Florio run over eleven laps.  Safety concerns and the oil crisis conspired to remove it from the world championship after 1973 and it was finally cancelled in 1977.  A much toned-down event is now run annually as a round of the Italian Rally Championship.

Further north, the thousand-mile Mille Miglia, also run on public roads, was first staged in 1927 and although soon one of the classic events on the calendar, it's the 1955 race to which a particular aura still attaches.  Won by Stirling Moss (1929-2020) and  Denis Jenkinson (1920-1996), they used a Mercedes 300SLR, a car which technically complied with the sports car regulations but was actually the factory's formula one machine (W196) with a bigger engine and a streamlined body with seats for two.  It wasn't exactly a "grand prix car with headlights" as some claimed but wasn't that far off.  Officially the W196S (Sports) in the factory register, for marketing purposes it was dubbed (add badged) as the 300SLR to add lustre to the 300SL Gullwing coupé then on sale.

Mercedes-Benz W196S (300SLR), Mille Miglia, 1955.

The race was completed in 10 hours, 7 minutes and 48 seconds, a average speed of 157.650 km/h (97.96 mph) (the course was never exactly 1000 miles and that year was 1,597 km (992 miles) and at times, the 300SLR touched almost 305 km/h (190mph) which enabled Moss to cover the last 340 km (211 miles) at an average speed of 265.7 km/h (165.1) mph.  The record set in 1955 will stand for all time because the Italian government banned the Mille Miglia after two fatal crashes during the 1957 event, one of which killed nine spectators and a cursory glace at the photographs showing crowds clustered sometimes literally inches from the speeding cars might suggest it's surprising not more died.  Today, the name of the Mille Miglia endures as a semi-competitive tour for historic racing cars which, run since 1977.  By contrast, events run on closed courses have survived, the most famous of which is the 24 Heures du Mans (the Le Mans 24 Hour) and well-known 1000 km, 12 & 24 hour races have been run at Sebring, Laguna Seca, Daytona, Bathurst, the Nürburgring and Spa Francorchamps.

Endurance racing: Porsche 917Ks sideways in the wet; Vic Elford (1935-2022, right #11) and Pedro Rodriguez (1940-1971, left #10), BOAC 1000km, Brands Hatch, April 1970.  The race was the third round of the 1970 World Sports Car Championship.  Chris Amon (1943–2016) put a Ferrari 512S on pole but the 1000 was won (by 5 laps) by Pedro Rodríguez & Leo "Leksa" Kinnunen (1943–2017) in a Porsche 917K entered by John Wyer (1909–1989).  Amon was impressed by the speed maintained by Rodríguez in atrociously wet conditions (although much improved from the lethally unstable version seen a year earlier, even by 1970 the 917 could be difficult to handle even on a dry surface) and is said to have remarked to his pit crew: "Can somebody tell Pedro it's raining?"

Some endurance required: In 2023, the Dowse Art Museum in Wellington, New Zealand, staged the exhibition exploring the 2014 installation at Fort Delta, Melbourne in July 2014 in which New Zealand based artist Claire Harris (b 1982) watched Ms Lohan's entire filmography back to back in a live performance art work over 28 hours.  The issues discussed included “how” and “why” and there were practical tips on developing the stamina required for such feats of endurance.  The companion 34 page illustrated book Happy birthday Lindsay Lohan, 2011-2014 is available on request from the National Library of New Zealand.  The pages are unnumbered, the rational for which is not disclosed.

As a general principle, an "endurance event" tends to be a longer version of something so it’s thus a relative as well as an absolute term.  In sport, something like the Marathon, run over 42 kilometres (26 miles) is the endurance event of running where as the shorter contests are sprints (such as the 100 or 200 meters) or “distance” races (such as the 5,000 or 10,000 metres).  However, were the Marathon not to exist, then the 10,000 would be the “endurance” event of the Olympic Games, the tag attaching to whatever is the longest form.  In other fields, “endurance” can be more nuanced because what some find an “act of endurance” to sit through, others relish and long for more.  Richard Wagner’s (1813–1883)'s Der Ring des Nibelungen (The Ring of the Nibelung, 1876 (usually referred to as “The Ring Cycle”)) is an opera of epic length in cycle consisting of four separate pieces, each of the composer regarded as “an opera”:

Das Rheingold: (The Rhinegold; some 2½ hours with no intermission)
Die Walküre: (The Valkyrie; some 4½-5½ hours with intermissions)
Siegfried: (some 5-5½ hours with intermissions)
Götterdämmerung: (Twilight of the Gods; some 5-6 hours with intermissions)

So, a performance of the Ring Cycle absorbs between 15-17 hours and is thus usually spread over several days, some productions staging the event across a month, each performance (usually three or four) held on a weekend.  Grand Opera really is the West’s greatest artistic achievement and among the aficionados, the Wagnerian devotees are the most dedicated and passionate, some travelling the world to compare and contrast different productions of the Ring.  For them it’s not usually a test of endurance (although a production of which they don’t approve will be a long 17 hours) because they relish every moment but for others it’s probably unthinkable.  Although it’s long been attributed to him, the US humorist Mark Twain (1835-1910) may never have said: “Wagner’s music isn’t as bad as it sounds”, the back-handed compliment reflects the view of the majority, brought up on shorter, more accessible forms of entertainment.  For them, one hour of Wagner would be an endurance test.

The three later individual pieces of The Ring are themselves epic-length operas and Wagner wrote a number in this vein including Die Meistersinger von Nürnberg (The Master-Singers of Nuremberg, 1868; 5-6 hours), Parsifal (1882; 4-5 hours), Lohengrin (1850; 4 hours), Tannhäuser (1845; 4 hours) and the incomparable Tristan und Isolde (1965; 4-5 hours).  What came to define “epic length” in Opera was: (1) the typical length of other works and (2) the powers of endurance of those on stage, in the orchestra pit or in the audience.  Other composers did tend to write shorter operas although Giacomo Meyerbeer (1791–1864), Giuseppe Verdi (1813–1901), Richard Strauss (1864–1949), Gioachino Rossini (1792–1868) and Hector Berlioz (1803–1869) all produced works running over four hours and it was not unusual for there to be two or even three intermissions.  For profligacy with time however, none match Wagner although some modern composers have written very long operas although their length seems other to be their only memorable feature.

Epics: On vinyl, tracks did lengthen and if the physical limits of vinyl were exceeded, the piece could be spread over more than one disk.  Iron Butterfly’s In-A-Gadda-Da-Vida (1968, left) was 17:05 in length, Jethro Tull’s Thick as a Brick (1972, centre) was 43:46 (over two disks) while Rush’s 2112 (1976, right) was 20:33.

Cast adrift from the moorings of endurance by internet streaming making available infinite playing time, “songs” in the twenty-first century can last literally hours and an illustrative example is The Rise and Fall of Bossanova by PC III (Michael J Bostwick) which weighs in at a Wagarian 13 hours, 23 minutes, and 32 seconds.  It seems between 2016-2020 to have held the Guinness World Record as the longest song officially released although whether this should be thought a proud boast or admission of guilt will be up to those who listen.  Ominously, one of the implications of AI (artificial intelligence) is that in theory, someone could release a song which, without hesitation, deviation or repetition, goes on forever.

Andy Warhol's Empire is occasionally screened but always on the basis that viewers may "come and go" at any point in its eight hour run-time.

In pop music, the “epic length piece” was shorter by virtue of technological determinism.  Modern pop music (as the term is now understood) began in the 1950s and the standard form of distribution by the 1960s was the LP (long-playing) vinyl album, first released in 1948.  Because the technology of the time limited the duration of music which could fit on the side of a LP disk to about 27 minutes, that became the upper limit for a single song and at that length, it could be called “epic length” or just “an epic”.  Some bands and individuals did produce “epics” with varied results and some were probably better enjoyed (or endured) with drugs.  Not discouraged by the limitations of vinyl, others noted the possibilities offered by double (2 disks) or even triple (3 disks) albums and penned “rock operas”, the need to change disks a convenient operatic touch in that it provided a intermission.  Andy Warhol (1928–1987) took the idea of the endurance test to celluloid, in 1965 releasing Empire, a silent film shot in black & white showing New York’s Empire State Building at night (form a single aspect).  Running for some eight hours and designed to be viewed in slow-motion, it received critical praise from the usual suspects and little interest among even those who frequented art-house cinemas.  Warhol issued as statement saying the purpose was “to see time go by” and it can’t be denied he succeeded, perhaps even more convincingly than his earlier five hour epic Sleep (1964) which was an edited collection of takes of a man sleeping.  Similar scenes may have been found among those who found watching Empire beyond their powers of endurance.

Mutual & Common

Mutual (pronounced myoo-choo-uhl)

(1) Possessed, experienced, performed, etc by each of two or more with respect to the other; reciprocal.

(2) Having the same relation each toward the other.

(3) Of or relating to each of two or more; held in common; shared.

(4) In corporate law, having or pertaining to a form of corporate organization in which there are no stockholders, and in which profits, losses, expenses etc, are shared by members in proportion to the business each transacts with the company:

(5) In informal use, an entity thus structured.

1470–1480: From the Middle English mutual (reciprocally given and received (originally of feelings)), from the Old & Middle French mutuel, from the Latin mūtu(us) (mutual, reciprocal (originally “borrowed”)), the construct being mūt(āre) (to change (source of the modern mutate (ie delta, omicron and all that))) + -uus (the adjectival suffix) + the Middle French -el (from the Latin –ālis (the third-declension two-termination suffix (neuter -āle) used to form adjectives of relationship from nouns or numerals) and rendered in English as –al.  Root was the primitive Indo-European mei- (to change, go, move).  The alternative spelling mutuall is obsolete.  Derived forms used to describe ownership structures such as quasi-mutual and trans-mutual are created as required.  Mutual & mutualist are nouns & adjectives, mutuality, mutualization, mutualism & mutualness are nouns, mutualize, mutualizing & mutualized are verbs and mutually & mutualistically are adverbs; the noun plural is mutuals.

The term "mutually exclusive" is widely used (sometimes loosely) but has a precise meaning in probability theory & formal logic where it describes multiple events or propositions such that the occurrence of any one dictates the non-occurrence of the other nominated events or propositions.  The noun mutualism is used in fields as diverse as corporate law, economic theory, materials engineering, political science and several disciplines within biology (where variously it interacts with and is distinguished from symbiosis).  The phrase "mutual admiration society" is from 1851 and appears to have been coined by Henry David Thoreau (1817–1862) to describe those who habitually were in agreement with each-other and inclined to swap praise.  The "mutual fund", although the structure pre-existed the adjectival use, is from 1950 and these soon came to be known simply as “mutuals”, the word appearing sometimes even in the registered names and the best known of the type were the building societies & benevolent (or friendly) societies, the core structural element of what was the ownership being held in common by the members rather than shareholders.  The concept of the mutual structure is of interest in some jurisdictions because of the suggestion the large assets held by chapters of the Freemasons may be so owned and, with the possibility the aging membership may ultimately result in these assets being dissolved and the proceeds distributed.  If, under local legislation, the structure was found to be mutual, membership might prove unexpectedly remunerative.

The Cold War's "mutually assured destruction" (MAD) is attested from 1963 (although it wasn’t until 1966 it entered general use) and was actually a modification of the Pentagon’s 1962 term “assured destruction” which was a technical expression from US military policy circles to refer to the number of deliverable nuclear warheads in the arsenal necessary to act as a deterrent to attack.  In the public consciousness it was understood but vaguely defined until 1965 when Robert McNamara (1916–2009; US Secretary of Defense 1961-1968) appeared before the House Armed Services Committee and explained the idea was "the minimum threat necessary to assure deterrence: the capability in a retaliatory nuclear attack to exterminate not less than one third the population of the Union of Soviet Socialist Republics (USSR)”.  The “mutual” was added as the number of deployable Soviet warheads reached a critical strategic mass.  The mastery of statistical analysis served McNamara well until the US escalation of the war in Vietnam when the Hanoi regime declined to conform to follow his carefully constructed models of behavior. 

In social media, a mutual is a pair of individuals who follow each other's social media accounts, whether by agreement or organically and there’s something a niche activity is working out the extent to which the behavior happens between bots.  Mutuality (reciprocity, interchange) was from the 1580s.  Mutually (reciprocally, in a manner of giving and receiving), was noted from the 1530s and the phrase mutually exclusive was first recorded in the 1650s.  The specialized mutualism (from the Modern French mutuellisme) dates from 1845, referring to the doctrine of French anarchist-socialist Pierre-Joseph Proudhon (1809-1865) that individual and collective well-being is attainable only by mutual dependence.  In the biological sciences, it was first used in 1876 to describe "a symbiosis in which two organisms living together mutually and permanently help and support one another" although there are those who differentiate mutualism (a type of co-existence where neither organism is directly affected by the other but the influence they exert on other organisms or the environment is of benefit to the other) from symbiosis (where there’s a co-dependency).

Parimutuel betting is from the French invention pari mutuel (mutual betting), the construct being pari (wager, from parier (to bet) from the Latin pariare (to settle a debt (literally “to make equal”)) from par, from paris (equal) + mutuel (mutual).  It describes a gambling system where all bets of a particular type are pooled and from this (gross-pool), taxes and the vigorish (from the Yiddish וויגריש‎ (vigrish), from the Russian вы́игрыш (výigryš) (winnings), the commission or “hose-take" are deducted.  The dividends are then calculated by dividing the remainder (net pool) by all winning bets.  In many jurisdictions it’s called the Tote after the totalisator, which calculates and displays bets already made; in Australia and New Zealand it’s the basis of the original agency structure of the Totalisator Agency Board (TAB).

The adoption of mutual as a synonym for "common" is from 1630s and was long condemned as being used “loosely, improperly and not infrequently, often by those who should know better”; “mutual friend" seemed the most common offence.  The view was that “mutual” could apply to only two objects and “common” should be used if three or more were involved.  Opinion has thankfully since softened.  Mutual and common (in the sense of the relation of two or more persons or things to each other) have been used synonymously since the sixteenth century and the use is considered entirely standard.  Objections are one of those attempts to enforce create rules in English which never existed, the only outcome being the choice of use treated as a class-identifier by those who care about such things and either ignored or un-noticed by most.  Tautologous use of mutual however should be avoided: One should say co-operation (not mutual co-operation) between two states.

Common (pronounced kom-uhn)

(1) Belonging equally to, or shared alike by, two or more or all in question (as in common property; common interests et al).

(2) Pertaining or belonging equally to an entire community, nation, or culture; public (as in common language; common history et al).

(3) Joint; united.

(4) Prevailing; Widespread; general; universal (eg common knowledge).

(5) Customary, habitual, everyday.

(6) In some jurisdictions a tract of land owned or used jointly by the residents of a community, usually a central square or park in a city or town (often as “the commons” or “the common”).

(7) In domestic & international law, the right or liberty, in common with other persons, to take profit from the land or waters of another, as by pasturing animals on another's land (common of pasturage ) or fishing in another's waters (common of piscary).  Of interest to economist and ecologists because of the disconnection between the economic gain from the commons and the responsibility for its care and management.

(8) Vulgar, ordinary, cheap, inferior etc (as a derogatory expression of class, often in phrases such as “common as muck” or “common as potatoes”, the back-handed compliment “the common-touch” applied to politicians best at disguising their contempt for the voters (or, as they refer to us: “the ordinary people”).

(9) In some (particularly Germanic) languages, of the gender originating from the coalescence of the masculine and feminine categories of nouns.

(10) In grammar, of or pertaining to common nouns as opposed to proper nouns.

(11) In the vernacular, referring to the name of a kind of plant or animal but its common (ie conversational) rather than scientific name (the idea reflected in the phrase “common or garden”).

(12) Profane; polluted (obsolete).

(13) Given to lewd habits; prostitute (obsolete).

(14) To communicate something; to converse, talk; to have sex; to participate; to board together; to eat at a table in common (all obsolete vernacular forms).

1250–1300: From the Middle English comun (belonging to all, owned or used jointly, general, of a public nature or character), from the Anglo-French commun, from the Old French, commun (Comun was rare in the Gallo-Romance languages, but reinforced as a Carolingian calque of the Proto-West Germanic gamainī (common) in the Old French and commun was the spelling adopted in the Modern French) (common, general, free, open, public), from the Latin commūnis (universal, in common, public, shared by all or many; general, not specific; familiar, not pretentious), thought originally to mean “sharing common duties,” akin to mūnia (duties of an office), mūnus (task, duty, gift), from the unattested base moin-, cognate with mean.  The Latin was from a reconstructed primitive Indo-European compound ḱom-moy-ni-s  (held in common), a compound adjective, the construct being ko- (together) + moi-n- (a suffixed form of the root mei- or mey (to change, go, move (hence literally "shared by all").  The second element of the compound was the source also of the Latin munia (duties, public duties, functions; specific office).  It was possibly reinforced in the Old French by the Germanic form of ḱom-moy-ni-s  (ko-moin-i) and influenced also the German gemein, and the Old English gemne (common, public).  Comun and its variations cam to displace the native Middle English imene & ȝemǣne (common, general, universal (from the Old English ġemǣne (common, universal)), and the later Middle English mene & mǣne (mean, common (also from the Old English ġemǣne)) and the Middle English samen & somen (in common, together (from the Old English samen (together)). A doublet of gmina.  Common is a noun, verb & adjective, commoner is a noun & adjective, commonality is a noun and commonly is an adverb; the noun plural is commons.

Common has been used disparagingly of women and criminals since at least the fourteenth century and snobs have added categories since as required.  The meanings "pertaining equally to or proceeding equally from two or more" & "not distinguished, belonging to the general mass" was from circa 1400 whereas the sense of "usual, not exceptional, of frequent occurrence" & "ordinary, not excellent" dates from the late fourteenth century.  Common prayer was that done in public in unity with other worshipers as contrasted with private prayer, both probably more common then than now.  The Church of England's Book of Common Prayer was first published in 1549 and went through several revisions for reasons both theological and political.  The 1662 edition remains the standard collection of the prayer books used in the Anglican Communion and while many churches now use versions written in more modern English, there remain traditionalists who insist on one of the early editions.

The common room was noted first in the 1660s, a place in the university college to which all members were granted common access.  The late fourteenth century common speech was used to describe both English and (less often) vernacular (which came to be called vulgar) Latin.  From the same time, the common good was an English adoption of the Latin bonum publicum (the common weal).  Common sense is from 1839 and is U whereas, because of the tortured grammar, 1848’s common-sensible is thought non-U.  The idea of common sense had been around since the fourteenth century but with a different meaning to the modern: The idea was of an internal mental power supposed to unite (reduce to a common perception) the impressions conveyed by the five physical senses (sensus communisin the Latin, koine aisthesis in the Ancient Greek). Thus it evolved into "ordinary understanding, without which one is foolish or insane" by the 1530s, formalised as "good sense" by 1726 with common-sense in the modern sense the nineteenth century expression.

The mid-fourteenth century common law was "the customary and unwritten laws of England as embodied in commentaries and old cases", as opposed to statute law.  Over the years, this did sometimes confuse people because in different contexts (common law vs statute law; common law versus equity; common law vs civil law) the connotations were different.  The phrase common-law marriage is attested from a perhaps surprisingly early 1909.  In the English legal system, common pleas was from the thirteenth century, from the Anglo-French communs plets (hearing civil actions by one subject against another as opposed to pleas of the crown).  In corporate law, common stock is attested from 1888.  The late fourteenth century commoner is from the earlier Anglo-French where in addition to conveying the expected sense of "one of the common people” also had the technical meaning “a member of the third estate of the estates-general".  In English it acquired the dual meaning as (1) of non-royal blood and (2), since the mid-fifteenth century “a member of the House of Commons”.  Commonly the adverb is from circa 1300 and commonness the noun from the 1520s though it originally meant only "state or quality of being shared by more than one", the idea of something of "quality of being of ordinary occurrence" not noted until the 1590s.  The adjective uncommon assumed a similar development, in the 1540s meaning "not possessed in common" and by the 1610s meaning "not commonly occurring, unusual; rare".

Last thoughts on a non-rule

The distinction between mutual (reciprocal; between two) and common (among three or more) probably once was, at least to some extent, observed by educated writers, Dr Johnson (1709-1984) in his A Dictionary of the English Language (1755) allowing but one definition: MUTUAL a. Reciprocal; each acting in return or correspondence to the other.

G K Chesterton.

That old curmudgeon G K Chesterton (1874-1936) was certainly convinced.  Writing about Charles Dickens (1812–1870) novel Our Mutual Friend (1864-1865), he claimed the title was the source of the phrase in general speech, snobbily noting of it was the “…old democratic and even uneducated Dickens who is writing here. The very title is illiterate. Any priggish pupil teacher could tell Dickens that there is no such phrase in English as 'our mutual friend'.  Anyone could tell Dickens that 'our mutual friend' means 'our reciprocal friend' and that 'our reciprocal friend' means nothing. If he had only had all the solemn advantages of academic learning (the absence of which in him was lamented by the Quarterly Review), he would have known better. He would have known that the correct phrase for a man known to two people is 'our common friend'."

The phrase in the English novel however pre-dated Dickens, Jane Austen (1775-1817) using it in both Emma (1816) and Persuasion (1818) and long before 1864, Mary Shelley (1797–1851), Sir Walter Scott (1771–1832), William Makepeace Thackeray (1811–1863), Herman Melville (1819–1891), James Fenimore Cooper (1789–1851) and Elizabeth Gaskell (1810–1865) all had “mutual friend” in their text.  Dickens, with the prominence afforded by the title and serialized in the press, doubtless popularized it and, as Chesterton well knew, literature anyway isn’t necessarily written in "common speech".  Whoever opened the floodgates, after 1864, mutual friends continued to flow, the writers George Orwell (1903-1950), Joseph Conrad (1857–1924), Jerome K Jerome (1859–1927), Rudyard Kipling (1865–1936), Mark Twain (1835-1910), Anthony Trollope (1815-1882), Henry James (1843–1916), Robert Louis Stevenson (1850–1894), Arthur Conan Doyle (1859–1930) and Church of England (broad faction) priest & historian Charles Kingsley (1819–1875) all content with "mutual friend" so those condemned by Chesterton are in good company.  The old snob probably did ponder if calling someone a “common friend” might create a misunderstanding but then, good with words, he’d probably avoid that by suggesting they were “rather common” or “a bit common" if that was what he wanted to convey, which not infrequently he often did.

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