Friday, April 22, 2022

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 ofBetter 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


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