Showing posts sorted by relevance for query Parabola. Sort by date Show all posts
Showing posts sorted by relevance for query Parabola. Sort by date Show all posts

Sunday, April 9, 2023

Parabola

Parabola (pronounced puh-rab-uh-luh)

(1) In geometry, a plane curve formed by the intersection of a right circular cone with a plane parallel to a generator of the cone; the set of points in a plane that are equidistant from a fixed line and a fixed point in the same plane or in a parallel plane. Equation: y2 = 2px or x2 = 2py.

(2) In rhetoric, the explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose; a parable.

1570s: From the Modern Latin parabola, from the Late Greek παραβολή (parabol) (a comparison; a setting alongside; parable (literally "a throwing beside" hence "a juxtaposition") so called by Apollonius of Perga circa 210 BC because it is produced by "application" of a given area to a given straight line.  The Greek parabol was derived from παραβάλλω (parabállō) (I set side by side”), from παρά (pará) (beside) + βάλλω (bállō) (I throw); a doublet of parable, parole, and palaver.  It had a different sense in Pythagorean geometry.  The adjectival form parabolic (figurative, allegorical, of or pertaining to a parable) from the Medieval Latin parabolicus from the Late Greek parabolikos (figurative) from parabolē (comparison) is now probably the most widely used.  In geometry, in the sense of “pertaining to a parabola”, it’s been in use since 1702.  A parabola is a curve formed by the set of points in a plane that are all equally distant from both a given line (called the directrix) and a given point (called the focus) that is not on the line.  It’s best visualised as a shape consisting of a single bend and two lines going off to an infinite distance.

Monza

On the Monza banking: Maserati 250F (left), Ferrari F555 Supersqualo (centre) & Vanwall VW2 (right).

The Autodromo Nazionale di Monza (National Automobile Racetrack of Monza) is now the fastest circuit still used in Formula One, the highest recorded speed the 231.5 mph (372.6 km/h) attained during qualifying for the 2005 Italian Grand Prix by a McLaren-Mercedes MP4-20 (in qualifying trim) on the long straight between the Lesmo corners and the Variante del Rettifilo.  Built in 1922, the Italian Grand Prix has been held there every year since 1949 except in 1980 when the track was being modernised and it’s a wonder the track has survived the attention of the Fédération Internationale de l'Automobile (the FIA; the International Automobile Federation).  Once an admirable body, the FIA has in recent decades degenerated into international sport’s dopiest regulatory body and has for some yers attempted to make motorsport as slow, quiet and processional as possible, issues like DEI (diversity, equity and inclusion) now apparently more important than quality of racing.  Set in the Royal Villa of Monza park and surrounded by forest, the complex is configured as three tracks: the 3.6 mile (5.8 kilometre) Grand Prix track, the 1.5 mile (2.4 kilometre) short circuit and the 2.6 mile (4.3 kilometre) high speed oval track with its famous steep bankings which was unused for decades left to fall into disrepair before it was restored in the 2010s.  The major features of the main Grand Prix track include the Curva Grande, the Curva di Lesmo, the Variante Ascari and the famous Curva Parabolica.

On the parabolica: 1966 Italian Grand Prix.

The Curva Parabolica (universally known as “the parabolica”) is the circuit’s signature corner, an increasing radius, long right-hand turn and the final corner before the main straight so the speed one can attain on the straight is determined essentially by the exit speed from the the parabolica; a perfect execution is thus essential for a quick lap.  Although in motorsport it’s common to discuss the lengths of straights, one notable statistic is that even at close to 150 mph (200 km/h) speed with with the fastest cars take the curve, to transit the the parabolica takes just over 7.6 seconds.  Improvements to both the cars and the circuit means it’s now a less dangerous place but many drivers have died in accidents at Monza, some on or approaching the parabolica including Wolfgang (Taffy) von Trips (1928–1961) and Jochen Rindt (1942-1970).  In 2021, the Monza authorities announced the parabolica officially would be renamed “Curva in honor of former Ferrari factory driver Michele Alboreto (1956-2001) who to date remains the last Italian driver to win a Formula One Grand Prix for Scuderia Ferrari.  It’s likely most will still refer to the curve as “the parabolica”.

The Monza circuit in its configuration for the 1955 Italian Grand Prix (left) and a Mercedes-Benz W196R (streamliner) exiting the parabolica ahead of two W196Rs in conventional open-wheel configuration.  The 1955 Italian Grand Prix was the seventh and final round of the World Championship of Drivers, the French, German, Swiss and Spanish events all cancelled in the aftermath of the disaster at Le Mans.  It was the fourth and last appearance of the Mercedes-Benz W196R streamliners which, after some bad experiences on the relatively tight Silverstone circuit, were restricted to the fast, open tracks.  Mercedes-Benz also withdrew from top-level competition after 1955 and, as a constructor, it would be half a century before they returned to Grand Prix racing.

The parabolic arc: A wheel drops off a Boeing Dreamlifter on take-off, describing a a classic parabolic arc.  The Boeing 747-400 Large Cargo Freighters (LCF) were created using a modified 747-400 airline frame and were most associated with their use carrying Boeing 787 Dreamliner parts between the US, Italy & Japan.  It was an unusual configuration in that it was required to carry components which while large, weren't particularly heavy.

Saturday, November 16, 2024

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 (parabol) (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 ντινομία (antinomía), the construct being ντι- (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))  + -́ (-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” et al) 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.

Wednesday, December 27, 2023

Perimeter & Parameter

Perimeter (pronounced puh-rim-i-ter)

(1) A line bounding or marking off an area; any boundary around.

(2) The outermost limits.

(3) In geometry, the border or outer boundary of a two-dimensional figure (the sum of the lengths of the segments that form the sides of a polygon.

(4) The total length of such line; the total length of any such closed curve, such as the circumference of a circle.

(5) In military jargon a fortified boundary that protects a position.

(6) In clinical ophthalmology, an instrument for determining the peripheral field of vision.

(7) In basketball, a semicircular line on a basketball court surrounding the basket, outside of which field goals are worth three points rather than two (also called three-point line).

(8) The area outside this line (often used attributively).

1585–1595: From the French périmètre (circumference, outer boundary, or border of a figure or surface), from the feminine Latin form perimetros, from the neuter Greek perímetron (circumference), the construct being peri- (around; about) + -meter from metron (measure), from the primitive Indo-European root me- (to measure).  The military sense of “boundary of a defended position” is said by some sources to have come into use only by 1943 despite the tactic being probably the second oldest military procedure still in use (the attack presumably the first).  Whether coincidental or not, the ultimate failure of perimeter defense was what finally led to the success of the Soviet offensive against the Nazi Sixth Army in Stalingrad (now Volgagrad) in 1943.  The technical terms created by the use of perimeter as a modifier include perimeter check (a patrol which checks to ensure a defensive perimeter remains in place) & perimeter fence.  Perimeter & perimetry are nouns, perimetral, perimetric & perimetrical are adjectives and perimetrically is an adverb; the noun plural is perimeters.

Parameter (pronounced puh-ram-uh-tuhr (U) or puh-ram-i-ter (non-U)

(1) In mathematics, a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).  (A value kept constant during an experiment, equation, calculation or similar, but varied over other versions of the experiment, equation, calculation etc).

(2) In mathematics, one of the independent variables in a set of parametric equations.

(3) In geometry, in the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.

(4) In crystallography, the ratio of the three crystallographic axes which determines the position of any plane; the fundamental axial ratio for a given species.

(5) In statistics, a variable entering into the mathematical form of any distribution such that the possible values of the variable correspond to different distributions (any measured quantity of a statistical population that summarizes or describes an aspect of the population).

(6) In computing, a variable that must be given a specific value during the execution of a program or of a procedure within a program.

(7) Limits or boundaries; guidelines; specifications; any constant, definitional or limiting factor (usually in the plural parameters).

(8) Characteristic or a factor; an aspect or element.

(9) In computing syntax for various purposes, an input variable of a function definition, that become an actual value (argument) at execution time (an actual value given to such a formal parameter).

1650-1660: From the French paramètre, from the New Latin parametrum (parameter), the construct being the Ancient Greek παρα- (para-) (beside, subsidiary) + μέτρον (métron) (meter) (measure), from the primitive Indo-European root me- (to measure).  The words was almost exclusive to mathematics & geometry until the late 1920s when it came to be extended to “measurable factor(s) which help to define a particular system", hence the now common alternative meaning “boundary, limit, characteristic factor” (under the influence of perimeter which used a similar spelling and (at least conceptually) could be understood to enjoy some overlap of meaning.  Although the wider definition has been in use since the 1950s, purists have never approved.  Parameter is a noun and parametric & parametrical are adjectives; the noun plural is parameters.

Parameters and perimeters

The more modern ways “parameter” has been used since the early twentieth century does offend the linguistically more fastidious but it seems clear the innovations are here to stay.  Some do however just get it wrong and university lecturers in the social sciences seem to be those who bear the heaviest burden of training a certain number of their institution’s first year students in the correct use of “parameter” & “perimeter”.  That they are sometimes confused is understandable because the spellings are so close and there is some sense of overlap in the meanings, both able to be used in a way which defines limits.  The definitions can be reduced to: (1) perimeter refers to either something physical (a national border; a fence etc) or a representation of something physical (lines on a map; the four sides of a square etc) whereas (2) a parameter is an element of specification, a constant or variable value which can be either an absolute value or a range.  So, a perimeter may be drawn on the basis of certain parameters while the values of parameters will in some cases exist within certain perimeters.  Definitions such as that are vague enough for those so inclined to find contradictions but for the way most people, most of the time (correctly) use parameter & perimeter, it seems serviceable.

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