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Third

Third is the ordinal numeral in the English language denoting the position or rank immediately succeeding the second and preceding the fourth in a sequence, series, or ordered list. It functions as an adjective, adverb, or noun to indicate relative placement, such as in rankings, dates (e.g., the third of the month), or measurements like the third floor of a building. Derived from Old English þridda, via metathesis from an earlier form related to Proto-Germanic *þridją-, the term traces its roots to Indo-European expressions for "three," reflecting its foundational role in numerical ordering systems across Germanic languages. In mathematical and fractional contexts, third commonly refers to one of three equal parts of a whole, expressed as "one-third" or 1/3, a usage essential in division, proportions, and everyday quantification such as dividing resources or analyzing sets. Beyond basic , the concept appears in specialized domains including , where a third interval spans three degrees in a (major or ), influencing and structures; mechanics, as in third gear for ; and narrative structure, denoting the third-person perspective in and . These applications underscore third's ubiquity in human and systems for , with no notable controversies but profound implications for logical sequencing and empirical in fields from statistics to .

Numerical and Mathematical Uses

Ordinal Designation

The ordinal "third" designates the position succeeding the second in a sequential order, corresponding to the integer 3 and used to indicate rank, arrangement, or progression in finite sets or lists. For instance, in enumerations, it identifies the element immediately after the initial pair, as in the third item of a series starting from the first. This usage extends to rankings, such as third place in competitions, where it reflects a defined hierarchy based on criteria like performance metrics. Etymologically, "third" originates from Late Old English þridda, a metathesis of Proto-Germanic *þridja-, meaning "next after the second," traceable to Proto-Indo-European *tréti̯os, an ordinal form derived from the root for "three." Unlike regular ordinals from fourth onward, which form by adding the suffix "-th" to the cardinal (e.g., four + th), "third" preserves an irregular Germanic pattern, avoiding a direct "three + th" construction due to historical phonetic shifts and analogical resistance in early English. This anomaly aligns with "first" and "second," which also deviate from the cardinal-plus-suffix model seen in higher numbers. In mathematical contexts, the finite ordinal "third" represents the third successor in the von Neumann construction of numbers, defined set-theoretically as the set containing the , its , and the of that : { \emptyset, {\emptyset}, {\emptyset, {\emptyset}} }. Abbreviated in numerals as "3rd" with the superscript "rd" (distinct from "th" for numbers like 4th or 13th), it follows English conventions for clarity in , though pronunciation remains "third" regardless of numeric form. These designations maintain consistency across disciplines, from basic counting to advanced ordering principles.

Fractional Representation

The unit fraction \frac{1}{3}, commonly referred to as "one-third," divides a whole into three equal parts, with a numerator of 1 indicating one such part and a denominator of 3 specifying the total divisions. This rational number is in lowest terms, as the greatest common divisor of 1 and 3 is 1, and it satisfies the property that \frac{1}{3} \times 3 = 1. In base-10 (decimal) notation, \frac{1}{3} expands to the non-terminating repeating decimal $0.\overline{3}, where the digit 3 repeats indefinitely; this arises because 3 is coprime to 10, preventing termination after finite digits and resulting in a repetend length of 1, the multiplicative order of 10 modulo 3. Equivalent representations include infinite series such as \sum_{n=1}^{\infty} 3 \times 10^{-n}, converging to exactly \frac{1}{3}. In contrast, positional representations in other bases depend on the prime factors of the denominator relative to the base: in base 3, \frac{1}{3} = 0.1_3 (terminating, as $3^{-1} = \frac{1}{3}); in base 2 (binary), it is the repeating $0.\overline{01}_2 = \sum_{k=1}^{\infty} 2^{-2k}, with period 2 due to the geometric series solution for division by 3 in powers of 2. These variations highlight how fractional representations of \frac{1}{3} are finite only in bases that are multiples of 3.

Geographical and Toponymic References

Urban Streets and Districts

In urban planning across the United States, streets designated as "Third Street" or "Third Avenue" commonly arise from 19th-century grid systems, where thoroughfares were sequentially numbered eastward or northward from a baseline such as a waterfront or central axis to simplify addressing and expansion. These grids, implemented in cities like New York, Philadelphia, and Los Angeles, prioritized efficiency in land division and infrastructure, with "third" indicating the position relative to primary reference lines. A notable example is Street Promenade in , which originated as a commercial corridor in the late within the city's early downtown core. Converted to a pedestrian-only mall on November 8, 1965, by developers including The Hahn Company to counter suburban retail flight, it initially struggled with design flaws but underwent a comprehensive redesign and reopening in 1989, evolving into a major open-air destination with over 30 million annual visitors by the early , featuring shops, theaters, and street performers. Urban districts named "Third Ward" trace to 19th-century municipal governance structures, where cities divided into wards for electoral and administrative purposes, with the third often encompassing working-class or industrial zones adjacent to central areas. In , , the Third Ward emerged as one of four original wards post-1836 incorporation, developing into a predominantly African American enclave southeast of downtown by the early 20th century, hosting pivotal community institutions like (founded 1947) and Emancipation Park (acquired 1872 as the first public park for freed slaves). It has sustained a legacy of amid demographic shifts, with a 2020 reflecting ongoing residential and cultural vitality. In , , the Historic Third Ward occupies a 10-block area south of Interstate 794 along the , originally a 19th-century warehouse and shipping hub that declined post-World War II . Revitalized in the through , it now functions as an and commerce district with preserved iron-clad buildings converted into galleries, over 100 restaurants, and the Milwaukee Public Market (opened 2005), drawing economic activity via events and the RiverWalk.

Other Locations

The Third Cataract of the constitutes a shallow, rapids-strewn stretch of the river in northern , positioned near Tombos (also known as Hannek) at approximately 19°45′N 30°22′E, where granite outcrops and rocky islands create navigational hazards amid faster-flowing waters. This feature, the third in a series of six cataracts extending from to , spans a region of exposed bedrock that constricts the river channel, historically limiting ancient trade and military movements upstream from into . Geological surveys identify the cataract's formations as granites, contributing to its turbulent and role as a natural barrier until modern damming altered flows elsewhere. Archaeological investigations reveal dense settlement patterns around the Third Cataract, with evidence of Ottoman-era frontiers and pre-pharaonic occupations influenced by the site's defensible terrain and resource access, including fortified zones established post-sixteenth-century Nile campaigns. The cataract's environs supported Kushite kingdoms, evidenced by rock inscriptions and burial sites dating to the second millennium BCE, underscoring its strategic importance in regional power dynamics. Unlike submerged upstream cataracts affected by , the Third remains largely intact, preserving its ecological niche for fish migration and riparian vegetation adapted to seasonal floods. Beyond the , the Third River in , exemplifies a smaller-scale waterway originating at the Great Notch Reservoir in Woodland Park (40°51′N 74°12′W) and extending about 7 miles southward through wooded and semi-rural corridors before tributary confluence with the . Hydrologic monitoring by the U.S. Geological Survey tracks discharge rates averaging 20-50 cubic feet per second, with peaks during regional storms reflecting its watershed's influences. This stream's derives from colonial-era sequencing of Passaic tributaries, and it sustains local including populations in its upper reaches, though pollution from upstream development has prompted restoration efforts since the 1990s.

Musical Applications

Theoretical Intervals and Chords

In music theory, the third is an spanning three degrees, such as from C to E in the scale. It qualifies as a major or minor , with the measuring three semitones and the measuring four semitones. These intervals form the basis of tertian harmony, where chords are constructed by stacking successive thirds above a root note. A major triad comprises a major third from the root to the mediant, followed by a minor third to the dominant, yielding a consonant sonority with a bright quality. Conversely, a minor triad features a minor third from the root followed by a major third, producing a darker timbre. Diminished and augmented triads extend this structure: the former stacks two minor thirds for a tense, unstable sound, while the latter uses two major thirds for symmetry and dissonance. The quality of a is primarily determined by the type of third above the , distinguishing from sonorities in tonal music. This third defines the chord's harmonic color, with alterations like suspensions replacing it temporarily to create tension resolved by restoration. In , these intervals approximate ratios, such as the third's and the third's 6:5, influencing perceived consonance.

Compositions and Recordings

Portishead's Third is a trip-hop and released on April 29, 2008, by the English Portishead on , featuring tracks that incorporate dissonant elements and electronic manipulation diverging from their earlier style. The album includes eleven compositions, such as "We Carry On" and "Machine Gun," produced by the band members , , and , emphasizing abrasive rhythms and vocal intensity. Soft Machine's Third, released in June 1970 by the English and band on Records, comprises a with side-long improvisational suites blending rock, , and structures. Key tracks include "Facelift" and "Moon in June," the latter featuring Robert Wyatt's vocals and guitar, marking the band's shift toward instrumental complexity before Wyatt's departure. Robert W. Jager's Third Suite for , composed in 1966 and published by Volkwein Bros., consists of three movements—"," "," and ""—designed for intermediate ensembles with rhythmic shifts and melodic accessibility suitable for contests and festivals. The work alternates meters, such as 4/4 and 3/4 in the march, and has been widely performed by school and community bands globally. The term "" denotes a genre of compositions fusing with classical forms, coined by in 1957 during a concert at the Lenox School of Jazz. Exemplary works include Schuller's own Seven Studies on Themes of (1959), which integrates serial techniques with jazz ensemble playing, and arrangements like Charles Mingus's orchestrated by Schuller for large jazz orchestra, premiered in 1989. These pieces prioritize structural rigor from alongside jazz's spontaneity, influencing subsequent hybrid ensembles.

Political and Ideological Contexts

Third Way Policies

Third Way policies, articulated primarily by sociologist in works such as The Third Way: The Renewal of (1998), sought to modernize by integrating market mechanisms with social protections, emphasizing "no rights without responsibilities" and an "enabling state" that invests in rather than passive provision. This approach rejected both state socialism's heavy interventionism and neoliberalism's minimal government, prioritizing equality of opportunity over outcome, fiscal prudence, and active labor market policies to reduce dependency. Core principles included promoting through and , conditional benefits tied to job-seeking obligations, and public-private partnerships to foster while addressing . In the , Tony Blair's government (1997–2007) implemented policies via the "welfare-to-work" agenda, including the programs launched in 1998, which provided job subsidies, training, and mandatory job search for the unemployed. The national minimum wage was introduced in 1999 at £3.60 per hour, rising to £5.52 by 2005, alongside tax credits for working families and increased child benefits. These measures correlated with unemployment falling from 7.6% in 1997 to 4.9% by 2001, and (measured before housing costs) declining from 26.1% in 1996–97 to 21% by 2004–05, though the 2010 target to halve it from 1998 levels was narrowly missed at 22%. Employment rates for lone parents rose from 44% in 1997 to 57% by 2007, attributed partly to policies, though critics from left-leaning sources argue persistent regional inequalities and later rebounds post-2008 undermined long-term gains. In the United States, Bill Clinton's administration advanced through the Personal Responsibility and Work Opportunity Reconciliation Act (PRWORA), signed on August 22, 1996, which replaced open-ended Aid to Families with Dependent Children (AFDC) with (TANF), imposing time limits (typically five years lifetime) and work requirements on recipients. This reform led to a 60% drop in caseloads, from 12.2 million recipients in 1996 to 4.9 million by 2002, with single-mother employment surging from 60% in 1994 to 75% by 2000. rates fell from 21.8% in 1996 to 16.2% by 2000, coinciding with , though empirical analyses indicate work incentives drove much of the employment rise while economic conditions amplified caseload reductions; deep poverty persisted for non-workers. Conservative-leaning evaluations, such as those from , credit PRWORA with fostering self-reliance, while progressive critiques highlight increased hardship during recessions due to block grants and state variability. Empirical outcomes across both nations demonstrate Third Way policies' success in boosting labor participation and curbing amid 1990s growth, with child poverty reductions averaging 300,000 fewer poor children annually from 1999–2010 via targeted transfers. However, causal attribution is complicated by concurrent booms; post-reform periods showed resilience in employment but vulnerability to downturns, as child poverty rose to 29% by 2010 after housing costs, and TANF failed to buffer the , serving only 26% of eligible poor families by 2016. These results underscore the approach's emphasis on conditional support yielding measurable behavioral shifts, though sustainability hinged on macroeconomic tailwinds rather than structural poverty eradication.

Third Position Ideologies

Third Position ideologies encompass a range of political doctrines that explicitly reject both liberal and Marxist communism, positioning themselves as a or alternative that prioritizes sovereignty, , and economic over internationalist or class-based paradigms. Core tenets include advocacy for corporatist economic models, where production is organized through state-mediated guilds or syndicates representing workers, employers, and the nation, aiming to eliminate class antagonism while subordinating private enterprise to collective goals. These ideologies often promote authoritarian , anti-globalism, and ethno-nationalist principles, viewing and as corrosive to organic social bonds. The intellectual origins trace to interwar European fascist movements, particularly Benito Mussolini's formulation of in during the 1920s and 1930s, which restructured the economy into 22 corporations under fascist oversight to foster national unity and reject both and unfettered markets. Mussolini's 1932 Labour Charter formalized this system, mandating collaboration between labor and capital to serve state imperatives, with strikes outlawed and production geared toward . Similar ideas appeared in other contexts, such as Otto Strasser's left-wing National Socialism in Germany, which critiqued big capital while upholding racial hierarchy, leading to his expulsion from the in 1930. Post-World War II, revived amid neo-fascist efforts to rebrand, distinguishing from orthodox Marxism-Leninism and ; for instance, Perón's Justicialism in from 1946 onward blended , social welfare, and , explicitly termed a "third position" between and . In the late 20th century, explicitly Third Positionist groups emerged in , such as the (ITP), founded in 1989 by former National Front members including , which advocated racial , inspired by , and opposition to both U.S. and Soviet . The ITP published the journal Third Path until the mid-1990s, promoting a "pan-European" while critiquing to appear more intellectual. Other variants include North Korea's ideology, self-described as transcending both systems via self-reliance and leader-centric since the 1950s. These ideologies differ from centrist "" policies, such as those of in the 1990s, which reconciled markets with without rejecting or . Critics from academic and anti-fascist perspectives, often affiliated with left-leaning institutions, classify Third Position as veiled due to its and exclusionary , though proponents argue it derives from first-principles critiques of in both and . Empirical outcomes in historical applications, like Italy's corporatist economy yielding limited growth before wartime collapse (industrial output rose 100% from 1922-1938 but stagnated post-Depression), underscore tensions between rhetoric and practical .

Third World Classification

The term "" was coined by French demographer Alfred Sauvy in an August 14, 1952, article published in the French weekly L'Observateur, where he drew an analogy to the Third Estate of pre-revolutionary to describe nations outside the dominant geopolitical blocs. Sauvy's formulation emphasized these countries as a revolutionary force ignored by the established powers, initially framing the classification in political rather than economic terms. During the , the Third World encompassed countries that remained neutral or non-aligned with either the —comprising the , , , and other capitalist democracies aligned via —or the Second World, which included the , its Eastern European satellites, and communist allies bound by the . This grouping, formalized through events like the 1955 and the 1961 founding of the , included diverse nations such as , , , and , many of which were post-colonial states seeking independence from superpower influence. Membership was determined by geopolitical stance rather than development levels, though the majority featured lower industrialization and reliance on primary commodities. Post-Cold War, particularly after , the term decoupled from its alignment-based origins and increasingly denoted economically underdeveloped or low-income countries, often those with high rates, limited , and dependence on foreign . This shift reflected the dissolution of bipolar divisions, leading organizations like the to classify similar nations using metrics such as GDP per capita below $1,085 (as of 2023 World Bank thresholds for low-income economies) or the UN's list, which identifies 46 nations based on income, human assets, and economic vulnerability indices. By the , "Third World" acquired pejorative connotations, prompting alternatives like "developing countries" or "Global South," though critics argue these evade the term's historical precision without addressing underlying causal factors like governance failures and resource mismanagement in many such states.

Additional Fields and Concepts

Sports and Competition

In competitive , the term "third" most frequently denotes the third-place finish, the awarded to athletes or teams that surpass all competitors except the winners of first and second place. This position is symbolized by medals in multi-event competitions such as the , where third-place finishers receive recognition for their performance, though without the prestige of gold or silver. In formats like association football's prior to , a dedicated third-place match pitted semi-final losers against each other to determine this , a practice discontinued in favor of direct semi-final outcomes but retained in some regional or club events. "Third string" refers to the tertiary group of players on a roster, positioned behind the primary starters (first string) and primary substitutes (second string), typically deployed in or scenarios rather than regular play. This hierarchy ensures depth, with third-string athletes often developing skills on junior varsity or reserve units; for instance, in , third-string quarterbacks may see limited snaps unless elevated due to performance or necessity. In , third base constitutes the infield position nearest the left foul line, approximately 90 feet from home plate, defended by the third baseman who must react swiftly to sharply hit grounders—a trait earning it the nickname "hot corner" due to the batter's proximity (90–120 feet). The role demands strong arm strength for throws to first base (127 feet away) and coverage of bunts or foul pops, with notable players like exemplifying defensive prowess through metrics such as outs above average. American football employs "third down" as the penultimate opportunity in a series of up to four downs to advance 10 yards for a new first down, often shifting strategies toward passing plays, especially in "third-and-long" situations (e.g., third down and 10+ yards remaining). Conversion rates on third down average around 40% league-wide in the , with defenses prioritizing pass rushes; for example, in 2024, teams like the Texans limited opponents to 32.14% third-down efficiency through aggressive schemes. Other contexts include the third division in hierarchical leagues (e.g., England's former Football League Third Division, now League Two, comprising professional clubs below the top tiers) and the third umpire in cricket, an off-field official using video replays for decisions like dismissals since the 1992–93 season. In legal contexts, the term "third party" denotes an individual or entity not originally involved in a contract, transaction, or dispute but affected by or intervening in it. For instance, a third-party beneficiary is someone who receives benefits from a contract made between others, enforceable under common law principles if intent is clear, as established in cases like Lawrence v. Fox (1859) in New York jurisprudence. Similarly, escrow arrangements involve a neutral third party holding assets until contractual conditions are met, a practice rooted in English equity law and codified in statutes like California's Civil Code Section 1624. A prominent incorporating "third" is the U.S. under the Fourth , which holds that individuals relinquish reasonable expectations of in information voluntarily disclosed to third parties, such as banks or providers. Originating in (1976), where subpoenaed bank records were deemed non-private, and reinforced in Smith v. (1979) regarding pen registers for phone numbers, the doctrine has faced scrutiny amid digital data proliferation but remains foundational, permitting warrantless access to such records absent newer limitations like those in (2018) for cell-site location data. "Jus tertii," a Latin term meaning "right of the third," allows a to assert a third party's legal rights as a , applied in disputes where possession derives from another's superior title. Socially, "third places" refer to informal gathering spots distinct from home (first place) and work (second place), facilitating community bonds through low-barrier interactions, as conceptualized by sociologist in his 1989 book The Great Good Place. Examples include libraries, bars, and parks, which empirical studies link to reduced isolation and enhanced , though urban decline has diminished many since the mid-20th century. In some societies, "" describes cultural or self-identified categories beyond male and female, with varying legal accommodations. India's recognized hijras and similar groups as a third gender in 2014, mandating quotas and document options, based on constitutional rights to and . Germany introduced a "diverse" marker in 2018 via the Third Gender Option Act, requiring medical verification initially but simplified in 2024 reforms. As of 2024, approximately 17 jurisdictions worldwide, including and , permit non-binary designations on passports or IDs, often driven by advocacy for self-identification, though biological sex remains dimorphic in per empirical reproductive , rendering such categories administrative rather than ontological.

Historical and Cultural Denotations

In the Estates-General of pre-revolutionary , the "Third Estate" denoted the broad category of commoners, encompassing peasants, artisans, merchants, and the rising , who constituted roughly 27 million individuals or 98 percent of the . This , burdened by heavy taxation and lacking the privileges of the First Estate () and Second Estate (), held only one vote in assemblies despite its numerical dominance, fueling grievances articulated in Abbé ' 1789 pamphlet What Is the Third Estate?, which argued the estate was the true embodiment of the nation. On June 17, 1789, Third Estate delegates, joined by reformist and nobles, declared themselves the , vowing on June 20 at the to draft a constitution, marking the onset of the Revolution. The "Third Rome" denoted Moscow's asserted role as the inheritor of imperial and Christian authority after the conquest of , the "Second Rome." III (r. 1462–1505) advanced this by marrying a princess and adopting the symbol, but the doctrine crystallized in a circa 1510–1521 from Philotheus to Vasily III, proclaiming "two Romes have fallen out, but the third stands firm—and there shall not be a fourth." This formulation positioned as the final guardian against and decline, justifying tsarist and as divinely ordained successors to the universal empire. In twentieth-century Germany, "Third Reich" denoted the National Socialist regime under from 1933 to 1945, framed as the culmination of Germanic imperial history following the (designated the "First Reich," 962–1806) and the Bismarckian (the "Second Reich," 1871–1918). The phrase originated in Arthur Moeller van den Bruck's 1923 book , which envisioned a spiritual renewal beyond , though the Nazis repurposed it for to evoke continuity and destiny amid post-World War I instability. Official usage waned after in favor of "Greater ," but the term persisted externally to signify the era's totalitarian structure and expansionist policies.

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