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.
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Xanax by Lindsay Lohan
Xanax lyrics Universal © Music Publishing Group
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