Interpolate & Extrapolate

Interpolate (pronounced in-tur-puh-leyt)

(1) To introduce (something additional or extraneous) between other things or parts; interject; interpose; intercalate; to make additions, interruptions, or insertions.

(2) In mathematics, to estimate (a value of a function) between the values already known or determined.

(3) To alter a text by the insertion of new matter (with a long history of being applied especially if done deceptively or without authorization but technically a neutral term and can be used either way).

(4) To insert (additional or spurious material) in this manner.

1605–1615: From the Latin interpolātus, past participle of interpolātus & interpolāre (to make new, refurbish, touch up; to give a new appearance to), the construct being inter- (between, among, together) + -polā- (verb stem (akin to polīre (to smooth or polish) + -tus (the past participle suffix) from polare, from the primitive Indo-European root pel- (to thrust, strike, drive), the connecting notion being "to full cloth".  The sense evolved in Latin from the neutral "refurbish" to the slightly more loaded "alter appearance of" to the actually accusative "falsify” (especially or specifically by adding new material".  By the early fifteenth century Middle English had gained interpolen in a similar sense and by the 1650s also interpolator, from the Late Latin interpolator (one who corrupts or spoils), agent noun from past participle stem of Latin interpolāre.  The noun interpolation (that which is interpolated) dates from the 1670s and appears to have evolved both from the seventeenth century French interpolation and directly from the Latin interpolationem (nominative interpolatio) from the past participle stem of interpolāre.  Interpolate, interpolated & interpolating are verbs, interpolater (or interpolator) & interpolation are nouns, interpolable, interpolatory, interpolative are adjectives and interpolatively is an adverb.

Extrapolate (pronounced ik-strap-uh-leyt)

(1) To infer (an unknown) from something that is known; an evidence-based conjecture.

(2) In statistics, to estimate (the value of a variable) outside the tabulated or observed range.

(3) In mathematics, to estimate (a function that is known over a range of values of its independent variable) to values outside the known range.

(4) To perform extrapolation.

1830s: The construct was extra- + -polate (extracted and borrowed from interpolate).  The verb extrapolate in the sense of “make an approximate calculation by inferring unknown values from trends in the known data" became popular among astronomers, statisticians, economists & mathematicians after appearing in an 1862 Harvard Observatory account of Comet Donati (Donati's Comet (C/1858 L1 & 1858 VI)) in 1858).  In contemporary accounts, it was said to have been a word used since the 1830s by English mathematician and astronomer Sir George Airy (1801-1892).  Extrapolation (an approximate calculation made by inferring unknown values from trends in the known data) dates from 1867 and was the noun of action from extrapolate by analogy with the long-established interpolation although the original sense was "an inserting of intermediate terms in a mathematical series", the transferred sense of "drawing of a conclusion about the future based on present tendencies" adopted since 1889.  Extrapolate, extrapolated & extrapolating are verbs, extrapolater (or extrapolator) & extrapolation are nous, extrapolable, extrapolatory, extrapolative are adjectives and extrapolatively is an adverb.

Extrapolation and Interpolation

The common root of the words is the Latin verb (polīre) meaning “to polish” which in this context means “adding finish” to a data-set by adding what’s missing but the prefix is most useful in distinguishing between the two, inter- meaning “between” or “among,” and extra-, “outside” or “beyond”.  The two words look similar and at first glance it’d be not unreasonable to assume they might be antonyms but, although related in use and tangled in history, they are used in different ways and, one highly nuanced and the other sometimes applied correctly but inducing the drawing of erroneous or at least misleading conclusions.  Interpolation refers to inserting something between other things, while extrapolation is the act of drawing conclusions about something unknown based on what is known.  In mathematics, the meanings are uncontroversial in that interpolation is the process of determining an unknown value within a sequence based on other points in that set, while extrapolation is the process of determining an unknown value outside of a set based on the existing data (often expressed as a “curve”).  Interpolation is a commonly used tool of mathematicians, statisticians and others in the data-based sciences where it’s necessary to determine a function’s value based on the value of other points, an unknown value within the sequence is determined based on what else is in the sequence.

Interpolation, used beyond mathematics can be a loaded word because it’s the act of introducing something (additional or extraneous) between other parts, usually in text or musical notation and thus the technical equivalent of “insert” or (sometimes) “interject or interpose”.  Interpolation can thus be a merely neutral description but because of the history of the word (in Latin it evolved from the neutral "refurbish" to the slightly more loaded "alter appearance of" to the actually accusative "falsify” (especially or specifically by adding new material"), can imply that what has been inserted is spurious, false, misleading or done with some other nefarious purpose.  It’s thus a word which needs to be used with caution lest implications be drawn where no inference was intended.

A big word with lots of syllables, interpolate may be unfamiliar to many and that’s maybe why sometimes it’s been used apparently in an attempt to impart some sense of gravitas or perhaps disguise what’s really happening.  In pop music, sampling, the interpolation of other people’s music into one’s own is now probably a sub-genre and it’s well understood although, despite the involvement of courts and copyright lawyers, the distinctions between sampling, interpretation and actual appropriation although well-trimmed, remain frayed at the margins and all three can be interpolated.  One derided as a form of plagiarism, sampling seems to have gained respectability, at least among those who practice the art, the critical legal device apparently being to sample by using a fragment from a previously recorded song, but re-recording rather than directly copying the original.  The origin of the practice appears to be as the work-around for when the copyright holder refuses to license the original for sampling purposes.  Use in this way, only a publisher’s permission is required although in some common-law jurisdictions, the original can be subject to a compulsory licensing regime.

Extrapolation is related to deduction, an act of drawing a conclusion about something unknown based on what is known so the verb extrapolate is often used synonymously with infer and deduce.  However, in mathematics, while the act of interpolation involves a closed data set with defined low and high values, extrapolation involves estimating the value of a variable or function outside an observed range so it can be necessary to understand the context (social, economic etc) of the numbers being used in the exercise.  A Roll-Royce dealership which has a good month and sells ten cars should probably not from that data-set extrapolate that in the year ahead they will sell 120; other factors need to be considered beyond the simple math.

Xanax (Alprazolam), a fast-acting benzodiazepine.  It is marketed as anti-anxiety medication.

Lindsay Lohan released the track Xanax in 2019.  With a contribution from Finnish pop star Alma (Alma-Sofia Miettinen; b 1996), the accompanying music video was said to be “a compilation of vignettes of life”, Xanax reported as being inspired by Ms Lohan’s “personal life, including an ex-boyfriend and toxic friends”.  Structurally, Xanax was quoted as being based around "an interpolation of" Better Off Alone, by Dutch Eurodance-pop collective Alice Deejay, slowed to a Xanax-appropriate tempo.

Lindsay Lohan risked going straight to Hell by creating a promotional meme featuring Pope Francis (b 1936; Roman Catholic Pope since 2013).  Cryptically captioned Blessed Be The Fruit, it included an image of the art-work used for her debut album Speak (2004).  Given the problems he's expected to manage, solve or conceal (depending on the circumstances), most would forgive the pope if he popped the odd Xanax.

The original photograph (top left) was taken in 2013 during a mass conducted in the Catedral Basílica do Santuário Nacional de Nossa Senhora Aparecida (Cathedral Basilica of the National Shrine of Our Lady Aparecida) in Aparecida, Brazil.  His Holiness was at the time administering communion.  It has since proved a popular photograph for meme-makers interpolating optical discs.

Xanax by Lindsay Lohan

I don't like the parties in LA, I go home

In a bad mood, pass out, wake up alone

Just to do it all over again, oh

Looking for you

Only one reason I came here

Too many people, I can't hear

Damn, I got here at ten

Now it's 4 AM

I can't be in this club

It's too crowded and I'm fucked

Ain't nobody here for love

Ain't nobody care about us

I got social anxiety, but you're like Xanax to me, yeah

Social anxiety, when you kiss me, I can't breathe

No, I can't be in this club

It's too crowded and I'm fucked

Ain't nobody here for love

Ain't nobody care 'bout us

 

I got social anxiety, but you're like Xanax to me, yeah

Social anxiety, when you kiss me, I can't breathe, yeah

 

But you're like Xanax to me

When you kiss me, I can't breathe

 

I try to stay away from you, but you get me high

Only person in this town that I like

Guess I can take one more trip for the night

Just for the night

 

Only one reason I came here

Too many people, I can't hear

Damn, I got here at ten

Now it's 4 AM

 

I can't be in this club

It's too crowded and I'm fucked

Ain't nobody here for love

Ain't nobody care about us

I got social anxiety, but you're like Xanax to me, yeah

Social anxiety, when you kiss me, I can't breathe

No, I can't be in this club

It's too crowded and I'm fucked

Ain't nobody here for love

Ain't nobody care 'bout us

 

I got social anxiety, but you're like Xanax to me, yeah

Social anxiety, when you kiss me, I can't breathe, yeah

 

But you're like Xanax to me

When you kiss me, I can't breathe

 

But you're like Xanax to me

When you kiss me, I can't breathe

Xanax lyrics Universal © Music Publishing Group

CONELRAD

CONELRAD (pronounced kon-ill-rad or kon-ill-rid)

As an acronym: CONtrol of ELectromagnetic RADiation, a Cold War era  system of emergency public broadcasting developed by the US in the mid 1950s.

Exclusive to the US, CONELRAD was a nationally standardized system of emergency public broadcasting (on the AM (amplitude modulation) medium-wave band at 640 & 1240 kHz) intended to operate in the event of enemy attack during the Cold War.  The original specifications for what emerged as CONELRAD was first discussed at the "Informal Government-Industry Technical Conference" (March, 1951) and later published by the FCC (Federal Communications Commission): "The primary plan for alerting broadcast stations that is currently being considered by the FCC Study Group is known as the Key Station System.  The arrangement requires certain telephone circuits (private wire or direct line to Toll Board) between the Air Defense Control Centers (ADCC) and specified radio stations to be known as Basic Key Stations & Relay Key Stations”.

Cold War PSA (public service announcement).

The essence of the system was each Basic Key Station upon receiving an alert or warning signal from the ADCC would, upon instruction, broadcast a predetermined message and also relay the message by telephone to all Relay Key Stations assigned to each Basic Key Station.  As a diversified network designed to be able to continue functioning even if various parts were destroyed, it was conceptually similar to a later US military project which would later evolve into the internet.  Intended to be simple, robust and able to reach as wide a possible audience in the shortest possible time, CONELRAD used simple protocols for alerting the public and other "downstream" stations, consisting of a sequence of shutting the station off for five seconds, returning to the air for five seconds, again shutting down for five seconds, and then transmitting a tone for 15 seconds.  Key stations would be alerted directly and all other broadcast stations would monitor a designated station in their area.

In the event of an attack on the US, all domestic television and FM (frequency modulation) radio stations were required immediately to cease broadcasting and upon alert, almost all AM stations shut down, those remaining on-air transmitting either on 640 or 1240 kHz.  No transmission would last more than a few minutes and upon one going “off-air” another would take over the frequency on a ”round robin” chain, this to confuse enemy aircraft which might be navigating using RDF (Radio Direction Finding), a technique first widely used in the early days of World War II (1939-1945).  In the US, all radio sets manufactured between 1953-1963 were required to have the two frequencies marked by the triangle-in-circle (CD Mark), the symbol of Civil Defense organizations.  In 1963, CONELRAD was replaced by the EBS (Emergency Broadcast System) which operated until 1997 when all responsibilities were assumed by the FCC.

Diet Coke product placement in Mean Girls (2004).  One of the clues in identifying product placement is that items carefully are placed so brand-names are always legible.

Product placement, a technique on marketing in which products are brands are “worked into” something like a film or television programmes, is now so ubiquitous (witness the frequent appearance in Mean Girls (2004) of Coca-Cola, Doritos, Cheetos, Dunkin' Donuts, Red Bull, Silk Milk, Taco Bell etc) that there are now internet sleuths gleefully who document each instance.  Frequently, the presence of a product is merely an example of “brand awareness” with no substantive effect on the plot (in most cases it’s of no significance whether the characters drive Fords or Buicks or drink Pepsi or Coca-Cola) although there have been some deemed morally or politically dubious and variously they’ve involved things like alcohol, tobacco or firearms or institutions like the US military.  Known also as “embedded marketing”, the technique is most associated with commercial cinema where the stuff is easy to interpolate but there have been examples even in literary fiction, the best known being The Bulgari Connection (2001) by Fay Weldon (1931-2023).  In that, in exchange for an undisclosed payment, the author was required to make a specified number of mentions of the Italian luxury goods house Bulgari (generously, greatly she exceeded the quota).  Of course, that’s an example which became notorious and it’s not known how many other “respectable” novelists have been subsidized this way.

Stromberg-Carlson radio (with CONELRAD settings arrowed in red) promoted as one of the many “plusses” in the ownership of one of the Ford Motor Company's new Edsels.  In Australia, the phrase “it seemed like a good idea at the time”  is known colloquially as the “streaker's defence”.

The companion technique is “product association”.  Here, a company seeks in some obvious way to be associated with someone or some institution and in every glossy magazine there will, in one form or another, be probably dozens of examples.  Usually, “product association” is contractual with the consideration (usually cash or some form of contra arrangement) flowing one way or the other but the technique can also be executed as a form of “ambush marketing” (a hotel hiring for a morning a number of Ferraris, Lamborghinis and such to park outside for a photo-shoot, thereby hoping the “prestige” of the brands will “rub off”, despite the manufacturers receiving not a peppercorn for their unwitting participation).  More conventionally, it’s a normal commercial transaction entered into on terms agreeable to both parties and, if thought mutually beneficial, it may be on the basis of NMA (no monetary action).  In the matter of Stromberg-Carlson (by then a division of General Dynamics, now famous for nuclear submarines, warplanes and such) advertising their satisfaction at their new “transistorized” radio with “Town-and-Country tuning” being “one of the outstanding plus features of America’s newest car, the exciting Edsel”, it would have seemed like a good idea at the time.  By all accounts the Stromberg-Carlson car radios were fine devices but exhorting customers to: “See and drive the Edsel – it’s wonderful!” would have done nothing to enhance the corporate image.  That is of course a risk with product association: just as positive image can rub off, if things go awry, there’s a risk of that spreading too.  As it was, the Edsel venture floundered within three seasons but Stromberg-Carlson wasn’t part of the collateral damage.

1958 Edsel Citation Convertible, a failure with a fine CONERAD transistorized radio by Stromberg-Carlson.

Formed in 1894 as a partnership between Swedish immigrants Alfred Stromberg (1861-1913) and Androv Carlson (1854-1925), Stromberg-Carlson was for much of the twentieth century one of the dominant US manufacturers and distributors of electronics and telecommunications equipment.  As is modern corporate practice, Stromberg-Carlson became absorbed into other concerns and has since been part of the swirl of M&A (mergers & acquisitions) activities but it remains active in the industry.  Between 1906-1907, Alfred Stromberg dissolved his interests in telecommunications and formed what would become the Stromberg Motor Devices Company and ultimately Stromberg Carburetors.  In the post-war years, Zenith-Stromberg carburetors were used on a variety of British cars but they became well-known in the US after being adopted in the late 1960s because the company had a product which was ideally suited to complying with the increasingly stringent US emission regulations, the trade-off being some loss of performance, particularly at higher engine speeds.  In something like the Jaguar E-Type (XKE; 1961-1971), the switch from triple SU carburetors to dual Zenith-Strombergs meant the high-speed response suffered but, even in those happier days, there weren't than many who with any frequency explored how the things performed above 125 mph (200 km/h).

Epitaph

Epitaph (pronounced ep-i-taf or ep-i-tahf)

(1) A commemorative inscription on a tomb or mortuary monument about the person buried at that site.

(2) A brief poem or written passage composed in commemoration of a dead person.

(3) A final judgment on a person or thing.

(4) To commemorate in or with an epitaph.

(5) To write or speak after the manner of an epitaph. 

1350–1400: From the Middle English epitaphe (inscription on a tomb or monument), from the Old French epitafe, from the twelfth century Old French epitaphe, from the Latin epitaphium (funeral oration, eulogy), from the Ancient Greek epitáphion (over or at a tomb; a funeral oration), (noun use of neuter of ἐπιτάφιος (epitáphios) ((words) spoken on the occasion of a funeral), the construct being epi- (From the Ancient Greek ἐπί (epí) (at, over; on top of; in addition to (in a special use in chemistry, it denotes an epimeric form))) + τάφος (táph(os)) (tomb) + -ion (the noun-adjectival suffix).  Táphos (tomb, burial, funeral) was related to taphē (interment) & thaptō (to bury) of uncertain origin.  It has long been thought derived (like the Armenian damban (tomb)) from the primitive Indo-European root dhembh- (to dig, bury) but recent scholarship has cast doubts and some etymologists suggest both the Armenian and Greek could be borrowings.  There were equivalent words in the Old English and regional variations were many; the one which survived longest was byrgelsleoð.

The companion words, which differ not only in nuance but in convention of use, include eulogy (an oration about the dead, delivered usually at a funeral or memorial service), obituary (something in written form published soon after death which provides a potted biography and epigraph (a quote engraved on a tombstone, variously plaintive, humorous or barbed).  Not quite the same but very to the point is the Latin hic jacet (literally “here lies”).  Epitaph is a noun or verb (used with object), epitaphic, epitaphial, epitaphed & epitaphless are adjectives, epitaphically is an adverb and epitaphist is a noun.  The noun plural is epitaphs.

,

Jonathan Swift's marble memorial, St Patrick's Cathedral, Dublin.

One of the most celebrated epitaphs in English was saeva indignatio (literally “savage indignation”) which appeared on the tomb of the delightfully wicked Anglo-Irish satirist & poet Jonathan Swift (1667-1745), expressing a resigned contempt at human folly.  Swift is probably best remembered for Gulliver's Travels (1726) but it was A Modest Proposal (1729) which defined the genre of satire and work in this vein is often still labeled "Swiftian".  Swift started his political life as a Whig but ended it a Tory, becoming an Anglican cleric who was appointed Dean of St Patrick's Cathedral, Dublin.

Swift not only wrote his own epitaph but left instructions also for the stonemason and the authorities of Saint Patrick’s Cathedral, the memorial to be rendered in black marble, mounted seven feet from the ground, the large letters to be deeply cut and strongly gilded.  His specifications were followed but the stridency of Swift's Latin displeased a few who, finding it harsh or inelegant, didn't always reproduce it with complete fidelity.  The translation into modern English is Here is laid the body of Jonathan Swift.....where savage indignation can no longer tear his heart. Depart, wayfarer, and imitate if you can a man who to his utmost strenuously championed liberty.  Fellow Irish poet William Butler Yeats (1865–1939) rendered it as the punchier Swift has sailed into his rest; savage indignation there cannot lacerate his breast.  Imitate him if you dare, world-besotted traveller; he served human liberty.

Epitaph (1990) by Charles Mingus (CBS–466631 2).

Charles Mingus (1922–1979) was an American double bassist, pianist, composer and bandleader and one of the seminal figures in jazz.  Although lauded for the way his bands would interpolate passages of collective improvisation into performance pieces, he was influential also in his structured compositions, some of which were, by the standards of the genre, unusually long.  None however matched his Epitaph, comprising over four-thousand measures (a grouping of beats, which indicates the meter of a particular piece of music) and demanding more than two hours to perform, ranking with epic-length pieces such as Wynton Marsalis’s (b 1961) Blood On The Fields (1997) and Carla Bley’s (b 1936) Escalator Over The Hill (1968-1971); only Wadada Leo Smith’s (b 1941) sprawling Ten Freedom Summers (2012), unfolding over five hours, runs longer.

It’s not clear how long Mingus worked on Epitaph and its gestation may have absorbed as long as Ten Freedom Summers (thirty-four years in the making) because fragments of Epitaph were performed as early as 1962 although whether it was then envisaged as what it became is unknown.  It was only after his death, while Mingus’s work was being catalogued, that the whole of Epitaph was assembled and the score compiled.  This enabled the piece to be performed in 1989 by a thirty-piece orchestra, conducted by Gunther Schuller (1925-2015) and produced by Mingus's widow, Sue Graham Mingus (b circa 1933).  It has since had a number of performances, several in 2007, and the complete score has been published.

Lindsay Lohan reading the epitaphs, graveyard scene in I know who killed me (2007).

Epitaph, full of melodies, is rewarding and not entirely unfamiliar because Mingus over the years included several snatches in live recordings and concerts preformed with smaller bands, playfully sampling the music of a few others in sections although that’s not typical of Epitaph, a work all have noted for its originality.  A two-hour suite for thirty-one musicians is not necessarily unwieldy but Epitaph is complicated and really demands a band both familiar with each-other and well-rehearsed.  It’s not the sort of piece suited to an ensemble, however virtuosic, assembled for a one-off performance and the definitive performance which one day will be released will likely have been carefully edited and polished from any number of studio sessions.  Technically, it’s challenging for a conductor, there are shifts between melodic strains which sometimes are sudden and sometimes overlap, parts apparently unresolved skid to a stop, tempos pick-up at various paces and there’s an underlying cross-talking between extreme-register instruments; doubtlessly it's no less difficult for the musicians, two pianists, two bassists, a drummer and two percussionists needing peacefully to co-exist although, this is Mingus and that means creative tension is lives between the notes.  Even once détente was established however, there's still the piece itself to conquer, not all of it in the familiar language of jazz for there are vertiginous jumps in register, fast phrases slurring effortlessly to the languid and the jar sometimes of the polytonality of which American composers of the twentieth century were so fond.  Critics and other aficionados of the art were enchanted but it’s suspected there were those who dipped in and out of their CD and listened just to the bits they liked.

Algorithm

Algorithm (pronounced al-guh-rith-um)

(1) A set of rules for solving a problem in a finite number of steps.

(2) In computing, a finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result.

(3) In mathematics and formal logic, a recursive procedure whereby an infinite sequence of terms can be generated.

1690s: From the Middle English algorisme & augrym, from the Anglo-Norman algorisme & augrimfrom, from the French algorithme, re-fashioned (under mistaken connection with Greek αριθμός (arithmos) (number)) from the Old French algorisme (the Arabic numeral system) from the Medieval Latin algorismus, a (not untypical) mangled transliteration of the Arabic ⁧الخَوَارِزْمِيّ⁩ (al-ḵawārizmiyy), the nisba (the part of an Arabic name consisting a derivational adjective) of the ninth century Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī and a toponymic name meaning “person from Chorasmia” (native of Khwarazm (modern Khiva in Uzbekistan)).  It was Muḥammad ibn Mūsā al-Khwārizmī works which introduced to the West some sophisticated mathematics (including algebra). The earlier form in Middle English was the thirteenth century algorism from the Old French and in English, it was first used in about 1230 and then by the English poet Geoffrey Chaucer (circa 1344-1400) in 1391.  English adopted the French term, but it wasn't until the late nineteenth century that algorithm began to assume its modern sense.  Before that, by 1799, the adjective algorithmic (the construct being algorithm + -ic) was in use and the first use in reference to symbolic rules or language dates from 1881.  The suffix -ic 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).  The noun algorism, from the Old French algorisme was an early alternative form of algorithm; algorismic was a related form.  The meaning broadened to any method of computation and from the mid twentieth century became especially associated with computer programming to the point where, in general use, this link is often thought exclusive.  The spelling algorism has been obsolete since the 1920s.  Algorithm, algorithmist, algorithmizability, algorithmocracy, algorithmization & algorithmics are nouns, algorithmize is a verb, algorithmic & algorithmizable are adjectives and algorithmically is an adverb; the noun plural is algorithms.

Babylonian and later algorithms

An early Babylonian algorithm in clay.

Although there is evidence multiplication algorithms existed in Egypt (circa 1700-2000 BC), a handful of Babylonian clay tablets dating from circa 1800-1600 BC are the oldest yet found and thus the world's first known algorithm.  The calculations described on the tablets are not solutions to specific individual problems but a collection of general procedures for solving whole classes of problems.  Translators consider them best understood as an early form of instruction manual.  When translated, one tablet was found to include the still familiar “This is the procedure”, a phrase the essence of every algorithm.  There must have been many such tablets but there's a low survival rate of stuff from 40 centuries ago not regarded as valuable.

So associated with computer code has the word "algorithm" become that it's likely a goodly number of those hearing it assume this was its origin and any instance of use happens in software.  The use in this context, while frequent, is not exclusive but the general perception might be it's just that.  It remains technically correct that almost any set of procedural instructions can be dubbed an algorithm but given the pattern of use from the mid-twentieth century, to do so would likely mislead or confuse confuse many who might assume they were being asked to write the source code for software.  Of course, the sudden arrival of mass-market generative AI (artificial intelligence) has meant anyone can, in conversational (though hopefully unambiguous) text, ask their tame AI bot to produce an algorithm in the syntax of the desired coding language.  That is passing an algorithm (using the structures of one language) to a machine which interprets the text and converts it to language in another structure, something programmers have for decades been doing for their clients.

A much-distributed general purpose algorithm (really more of a flow-chart) which seems so universal it can be used by mechanics, programmers, lawyers, physicians, plumbers, carpet layers, concreting contractors and just about anyone whose profession is object or task-oriented.   

The AI bots have proved especially adept at such tasks.  While a question such as: "What were the immediate implications for Spain of the formation of the Holy Alliance?" produces varied results from generative AI which seem to range from the workmanlike to the inventive, when asked to produce computer code the results seem usually to be in accord with a literal interpretation of the request.  That shouldn't be unexpected; a discussion of early nineteenth century politics in the Iberian Peninsular is by its nature going to to be discursive while the response to a request for code to locate instances of split infinitives in a text file is likely to vary little between AI models.  Computer languages of course impose a structure where syntax needs exactly to conform to defined parameters (even the most basic of the breed such as that PC/MS-DOS used for batch files was intolerant of a single missing or mis-placed character) whereas something like the instructions to make a cup of tea (which is an algorithm even if not commonly thought of as one) greatly can vary in form even though the steps and end results can be the same.

An example of a "how to make a cup of tea" algorithm.  This is written for a human and thus contains many assumptions of knowledge; one written for a humanoid robot would be much longer and include steps such as "turn cold tap clockwise" and "open refrigerator door".

The so-called “rise of the algorithm” is something that has attracted much comment since social media gained critical mass; prior to that algorithms had been used increasingly in all sorts of places but it was the particular intimacy social media engenders which meant awareness increased and perceptions changed.  The new popularity of the word encouraged the coining of derived forms, some of which were originally (at least to some degree) humorous but beneath the jocularity, many discovered the odd truth.  An algorithmocracy describes a “rule by algorithms”, a critique in political science which discusses the implications of political decisions are being made by algorithms, something which in theory would make representative and responsible government not so much obsolete as unnecessary.  Elements of this have been identified in the machinery of government such as the “Robodebt” scandal in Australia in which one or more algorithms were used to raise and pursue what were alleged to be debts incurred by recipients of government transfer payments.  Despite those in charge of the scheme and relevant cabinet ministers being informed the algorithm was flawed and there had been suicides among those wrongly accused, the politicians did nothing to intervene until forced by various legal actions.  While defending Robodebt, the politicians found it very handy essentially to disavow connection with the processes which were attributed to the algorithm.

The feeds generated by Instagram, Facebook, X (formerly known as Twitter) and such are also sometimes described as algorithmocracies in that it’s the algorithm which determines what content is directed to which user.  Activists have raised concerns about the way the social media algorithms operate, creating “feedback loops” whereby feeds become increasingly narrow and one-sided in focus, acting only to reinforce opinions rather than inform.  In fairness, that wasn’t the purpose of the design which was simply to keep the user engaged, thereby allowing the platform to harvest more the product (the user’s attention) they sell to consumers (the advertisers).  Everything else is an unintended consequence and an industry joke was the word “algorithm” was used by tech company CEOs when they didn’t wish to admit the truth.  A general awareness of that now exists but filter bubbles won’t be going away but what it did produce were the words algorithmophobe (someone unhappy or resentful about the impact of algorithms in their life) and algorithmophile (which technically should mean “a devotee or admirer of algorithms” but is usually applied in the sense of “someone indifferent to or uninterested in the operations of algorithms”, the latter represented by the great mass of consumers digitally bludgeoned into a state of acquiescent insensibility.

Some of the products are fighting back: The Algorithm: How AI Decides Who Gets Hired, Monitored, Promoted, and Fired and Why We Need to Fight Back Now (2024) by  by Hilke Schellmann, pp 336, Hachette Books (ISBN-13: 978-1805260981).

Among nerds, there are also fine distinctions.  There are subalgorithms (sub-algorithm seems not a thing) which is a (potentially stand-alone) algorithm within a larger one, a concept familiar in many programming languages as a “sub-routine” although distinct from a remote procedure call (RPC) which is a subroutine being executed in a different address space.  The polyalgorithm (again hyphens just not cool) is a set of two or more algorithms (or subalgorithms) with instructions for choosing which in some way integrated.  A very nerdy dispute does exist within mathematics and computer science around whether an algorithm, at the definitional level, really does need to be restricted to a finite number of steps.  The argument can eventually extend to the very possibility of infinity (or types of infinity according to some) so it really is the preserve of nerds.  In real-world application, a program is an algorithm only if (even eventually), it stops; it need not have a middle but must have a beginning and an end.

There is also the mysterious pseudoalgorithm, something les suspicious than it may first appear.  Pseudoalgorithms exist usually for didactic purposes and will usually interpolate (sometime large) fragments of a real algorithm bit it may be in a syntax which is not specific to a particular (or any) programming language, the purpose being illustrative and explanatory.  Intended to be read by humans rather than a machine, all a pseudoalgorithm has to achieve is clarity in imparting information, the algorithmic component there only to illustrate something conceptual rather than be literally executable.  The pseudoalgorithm model is common in universities and textbooks and can be simplified because millions of years of evolution mean humans can do their own error correction on the fly.

Of the algorithmic

The Netflix algorithm in action: Lindsay Lohan (with body-double) during filming of Irish Wish (2024).  The car is a Triumph TR4 (1961-1967), one of the early versions with a live rear axle, a detail probably of no significance in the plot-line.

The adjective algorithmic has also emerged as an encapsulated criticism, applied to everything from restaurant menus, coffee shop décor, choices of typefaces and background music.  An entire ecosystem (Instagram, TikTok etc) has been suggested as the reason for this multi-culture standardization in which a certain “look, sound or feel” becomes “commoditised by acclamation” as the “standard model” of whatever is being discussed.  That critique has by some been dismissed as something reflective of the exclusivity of the pattern of consumption by those who form theories about what seem not very important matters; it’s just they only go to the best coffee shops in the nicest parts of town.  In popular culture though the effect of the algorithmic is widespread, entrenched and well-understood and already the AI bots are using algorithms to write music will be popular, needing (for now) only human performers.  Some algorithms have become well-known such as the “Netflix algorithm” which presumably doesn’t exist as a conventional algorithm might but is understood as the sets of conventions, plotlines, casts and themes which producers know will have the greatest appeal to the platform.  The idea is nothing new; for decades hopeful authors who sent manuscripts to Mills & Boon would receive one of the more gentle rejection slips, telling them their work was very good but “not a Mills & Boon book”.  To help, the letter would include a brochure which was essentially a “how to write a Mills & Boon book” guide and it included a summary of the acceptable plot lines of which there were at one point reputedly some two dozen.  The “Netflix algorithm” was referenced when Falling for Christmas, the first fruits of Lindsay Lohan’s three film deal with the platform was released in 2022.  It was an example of followed a blending of several genres (redemption, Christmas movie, happy ending etc) and the upcoming second film (Irish Wish)  is of the “…always a bridesmaid, never a bride — unless, of course, your best friend gets engaged to the love of your life, you make a spontaneous wish for true love, and then magically wake up as the bride-to-be.” school; plenty of familiar elements there so it’ll be interesting to see if the algorithm was well-tuned.

Math of the elliptic curve: the Cox–Zucker machine can help.

Some algorithms have become famous and others can be said even to have attained a degree of infamy, notably those used by the search engines, social media platforms and such, the Google and TikTok algorithms much debated by those concerned by their consequences.  There is though an algorithm remembered as a footnote in the history of linguistic oddities and that is the Cox–Zucker machine, published in 1979 by Dr David Cox (b 1948) and Dr Steven Zucker (1949–2019).  The Cox–Zucker machine (which may be called the CZM in polite company) is used in arithmetic geometry and provides a solution to one of the many arcane questions which only those in the field understand but the title of the paper in which it first appeared (Intersection numbers of sections of elliptic surfaces) gives something of a hint.  Apparently it wasn’t formerly dubbed the Cox–Zucker machine until 1984 but, impressed by the phonetic possibilities, the pair had been planning joint publication of something as long ago as 1970 and undergraduate humor can’t be blamed because they met as graduate students at Princeton University.  The convention in academic publishing is for authors’ surnames to appear in alphabetical order and the temptation proved irresistible.

Parole

Parole (pronounced puh-rohl or pa-rawl (French))

(1) In penology, the (supervised) conditional release of an inmate from prison prior to the end of the maximum sentence imposed.

(2) Such a release or its duration.

(3) An official document authorizing such a release (archaic except as a modifier).

(4) In military use, the promise (usually in the form of a written certificate) of a prisoner of war, that if released they either will return to custody at a specified time or will not again take up arms against their captors.

(5) Any password given by authorized personnel in passing by a guard (archaic but still used in video gaming).

(6) In military use, a watchword or code phrase; a password given only to officers, distinguished from the countersign, given to all guards (archaic but still used in video gaming).

(7) A word of honor given or pledged (archaic).

(8) In US immigration legislation, the temporary admission of non-U.S. citizens into the US for emergency reasons or on grounds considered in the public interest, as authorized by and at the discretion of the attorney general.

(9) In structural linguistics, language as manifested in the individual speech acts of particular speakers (ie language in use, as opposed to language as a system).

(10) To place or release on parole.

(11) To admit a non-US citizen into the US as provided for in the parole clauses in statute.

(12) Of or relating to parole or parolees:

(13) A parole record (technical use only).

1610–1620: From the Middle French parole (word, formal promise) (short for parole d'honneur (word of honor)), from the Old French parole, from the Late Latin parabola (speech), from the Classical Latin parabola (comparison), from the Ancient Greek παραβολή (parabolḗ) (a comparison; parable (literally “a throwing beside”, hence “a juxtaposition").  The verb was derived from the noun an appeared early in the eighteenth century; originally, it described “what the prisoner did” (in the sense of a “pledge”) but this sense has long been obsolete.  The transitive meaning “put on parole, allow to go at liberty on parole” was in use by the early 1780s while the use to refer to “release (a prisoner) on his own recognizance” doesn’t appear for another century.  The adoption in English was by the military in the sense of a “word of honor” specifically that given by a prisoner of war not to escape if allowed to go about at liberty, or not to take up arms again if allowed to return home while the familiar modern sense of “a (supervised) conditional release of a inmate before their full term is served” was a part of criminal slang by at least 1910.  An earlier term for a similar thing was ticket of leave.  In law-related use, parol is the (now rare) alternative spelling.  Parole is a noun & verb, parolee is a noun, paroled & paroling are verbs and parolable, unparolable, unparoled & reparoled are adjectives (hyphenated use is common); the noun plural is paroles.

A parole board (or parole authority, parole panel etc) is panel of people who decide whether a prisoner should be released on parole and if released, the parolee is placed for a period under the supervision of a parole officer (a law enforcement officer who supervises offenders who have been released from incarceration and, often, recommends sentencing in courts of law).  In some jurisdictions the appointment is styled as “probation officer”.  The archaic military slang pass-parole was an un-adapted borrowing from French passe-parole (password) and described an order passed from the front to the rear by word of mouth. Still sometimes used in diplomatic circles, the noun porte-parole (plural porte-paroles) describes “a spokesperson, one who speaks on another's behalf” and was an un-adapted borrowing from mid sixteenth century French porte-parole, from the Middle French porteparolle.

The Parole Evidence Rule

In common law systems, the parol evidence rule is a legal principle in contract law which restricts the use of extrinsic (outside) evidence to interpret or alter the terms of a written contract.  The operation of the parol evidence rule means that if two or more parties enter into a written agreement intended to be a complete and final expression of their terms, any prior or contemporaneous oral or written statements that contradict or modify the terms of that written agreement cannot be used in court to challenge the contract’s provisions.  The rule applies only to properly constructed written contracts which can be regarded as “final and complete written agreements” and the general purpose is to protect the integrity of the document.  Where a contract is not “held to be final and complete”, parol evidence may be admissible, including cases of fraud, misrepresentation, mistake, illegality or where the written contract is ambiguous.  The most commonly used exceptions are (1) Ambiguity (if a court declares a contract term ambiguous, external evidence may be introduced to to clarify the meaning), (2) Void or voidable contracts (if a contract was entered into under duress or due to fraud or illegality, parol evidence can be used to prove this.  In cases of mistakes, the scope is limited but it can still be possible), (3) Incomplete contracts (if a court determines a written document doesn’t reflect the full agreement between the parties, parol evidence may be introduced to “complete it”, (4) Subsequent agreements (modifications or agreements made after the written contract can generally be proven with parol evidence although in the narrow technical sense such additions may be found to constitute a “collateral contract”.

Parole & probation

Depending on the jurisdiction, “parole” & “probation” can mean much the same thing or things quite distinct, not helped by parolees in some places being supervised by “probation officers” and vice versa.

In the administration of criminal law, “parole” and “probation” are both forms of supervised release but between jurisdictions the terms can either mean the same thing or be applied in different situations.  As a general principle, parole is the conditional release of a prisoner before completing their full sentence and those paroled usually are supervised by a parole officer and must adhere to certain conditions such as regular meetings, drug testing and maintaining employment and certain residential requirements.  The purpose of parole is (1) a supervised reintegration of an inmate into society and (2) a reward for good behavior in prison.  Should a parolee violate the conditions of their release, they can be sent back to prison to serve the remainder of their sentence.  As the word typically is used, probation is a court-ordered period of supervision in the community instead of, or in addition to, a prison sentence.  A term of probation often imposed at sentencing, either as an alternative to incarceration or as a portion of the sentence after release.  Like parolees, individuals on probation are monitored, often by a probation officer (although they may be styled a “parole officer”) and are expected to follow specific conditions.  Probation is in many cases the preferred sentencing option for first offenders, those convicted of less serious offences and those for whom a custodial sentence (with all its implications) would probably be counter-productive.  It has the advantage also of reducing overcrowding in prisons and is certainly cheaper for the state than incarceration.  Those who violate the terms of their probation face consequences such as an extended probation or being sent to jail.  The word “parole” in this context was very much a thing of US English until the post-war years when it spread first to the UK and later elsewhere in the English-speaking world.

Langue & parole

In structural linguistics, the terms “langue” & “parole” were introduced by the groundbreaking Swiss semiotician Ferdinand de Saussure (1857-1913) and remain two of the fundamental concepts in the framework of structuralism and are treated as important building blocks in what subsequently was developed as the science of human speech.  Within the profession, “langue” & “parole” continue to be regarded as “French words” because the sense in that language better describes things than the English translations (“language” & “speech” respectively) which are “approximate but inadequate”.  Langue denotes the system (or totality) of language shared by the “collective consciousness” so it encompasses all elements of a language as well as the rules & conventions for their combination (grammar, spelling, syntax etc).  Parole is the use individuals make of the resources of language, which the system produces and combines in speech, writing or other means of transmission.  As de Saussure explained it, the conjunction and interaction of the two create an “antinomy of the social and shared”, a further antinomy implied in the idea that langae is abstract and parole is concrete.

The construct of the noun antinomy was a learned borrowing from the Latin antinom(ia) + the English suffix “-y” (used to form abstract nouns denoting a condition, quality, or state).  The Latin antinomia was from the Ancient Greek ἀντινομία (antinomía), the construct being ἀντι- (anti- (the prefix meaning “against”), ultimately from the primitive Indo-European hent- (face; forehead; front)) + νόμος (nómos) (custom, usage; law, ordinance) from  νέμω (némō) (to deal out, dispense, distribute), from the primitive Indo-European nem- (to distribute; to give; to take))  + -ῐ́ᾱ (-íā) (the suffix forming feminine abstract nouns).  The English word is best understood as anti- (in the sense of “against”) +‎ -nomy (the suffix indicating a system of laws, rules, or knowledge about a body of a particular field).  In law, it was once used to describe “a contradiction within a law, or between different laws or a contradiction between authorities” (a now archaic use) but by extension it has come to be used in philosophy, political science and linguistics to describe “any contradiction or paradox”.  A sophisticated deconstruction of the concept was provided by the German German philosopher Immanuel Kant (1724–1804) who in Kritik der reinen Vernunft (Critique of Pure Reason (1781)) explained that apparent contradictions between valid conclusions (a paradox) could be resolved once it was understood the two positions came from distinct and exclusive sets, meaning no paradox existed, the perception of one merely the inappropriate application of an idea from one set to another.

So langue is what people use when thinking and conceptualizing (abstract) while parole what they use in speaking or writing (concrete), Saussure’s evaluative distinction explained as “The proper object of linguistic study is the system which underlies any particular human signifying human practice, not the individual utterance.” and the implication of that was that langue is of more importance than parole.  In the English-speaking world, it was the work of US Professor Noam Chomsky (b 1928) which made the concept of langue & parole well-known through his use of the more accessible terms “competence” & “performance”.  Chomsky’s latter day role as a public intellectual (though a barely broadcasted one in his home country) commenting on matters such as US foreign policy or the contradictions of capitalism has meant his early career in linguistics is often neglected by those not in the profession (the highly technical nature of the stuff does mean it’s difficult for most to understand) but his early work truly was revolutionary.

Noam Chomsky agitprop by Shepard Fairey (b 1970) on Artsy.

Chomsky used “competence” to refer to a speaker's implicit knowledge of the rules and principles of a language, something which permits them to understand and generate grammatically correct sentences which can be understood by those with a shared competence.  Competence is the idealized, internalized system of linguistic rules that underlies a speaker's ability to produce and comprehend language. It reflects one’s mental grammar, independent of external factors like memory limitations or social context.  Performance refers to the actual use of language IRL (in real life), influenced by psychological and physical factors such as memory, attention, fatigue, and social context.  Performance includes the errors, hesitations, and corrections that occur in everyday speech and Chomsky made the important point these do not of necessity reveal lack of competence.  Indeed, understood as “disfluencies”, (the “ums & ahs” etc) these linguistic phenomenon turned out to be elements it was essential to interpolate into the “natural language” models used to train AI (artificial intelligence) (ro)bots to create genuinely plausible “human analogues”.  Chomsky argued competence should be the primary domain of inquiry for theoretical linguistics and he focused on these abstract, universal principles in his early work which provoked debates which continue to this day.  Performance, subject to errors, variability and influenced by non-linguistic factors, he declared better studied by those in fields like sociolinguistics and psycholinguistics.