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Absolute

The is a foundational in metaphysics, referring to the complete, self-contained, and all-encompassing that underlies all , independent of any external conditions or relations. This notion posits an ultimate of and unchanging permanence, serving as the ground from which finite phenomena derive without itself being contingent or derived. In Western philosophy, the Absolute gained prominence through Baruch Spinoza's identification of it with a singular, infinite substance possessing infinite attributes, where God or Nature constitutes the self-caused totality of reality, rejecting dualistic separations between creator and creation. G.W.F. Hegel further developed it as the Absolute Spirit or Absolute Idea, a dynamic process of dialectical self-unfolding through thesis, antithesis, and synthesis, culminating in the rational comprehension of the whole of reality in history, art, religion, and philosophy. Earlier antecedents appear in Plotinus's The One, an emanative source beyond being and multiplicity, and parallels exist in Eastern traditions such as Advaita Vedanta's as non-dual consciousness. The concept has defined Absolute Idealism, emphasizing mind or reason as the fundamental reality, influencing 19th-century via Hegel and F.W.J. Schelling, though it provoked controversies over its implications for —equating the Absolute with an impersonal totality risked , while personalist interpretations aligned it with divine . Critiques, notably from empiricists and positivists, highlight its unverifiability through sensory data, arguing that positing an unconditioned whole invites speculative abstraction detached from causal observation, with figures like Nietzsche rejecting it amid the decline of metaphysical absolutes in favor of perspectival truths. Despite such challenges, the Absolute persists in debates on foundational , underscoring tensions between rational deduction of necessary being and empirical prioritization of contingent relations.

Philosophy and Theology

The Absolute in philosophy

The Absolute in philosophy refers to the foundational, unconditioned reality posited as the ground and totality of existence, free from relational dependencies or limitations. This metaphysical emphasizes a self-subsistent that accounts for the and underlying apparent in the , often contrasting with empirical or pluralistic ontologies. It gained prominence in post-Cartesian and , where it served as the apex of systematic philosophy, though its formulations vary: as static substance in Spinoza, dynamic process in Hegel, or intuitive identity in Schelling. Baruch Spinoza (1632–1677) articulated the Absolute as the singular, infinite substance Deus sive Natura (God or Nature), self-caused (causa sui) and possessing infinite attributes, of which extension and thought are knowable to humans. In his (1677), all finite modes—particular entities—are modifications of this substance, following necessarily from its essence, rendering the universe a deterministic expression of the Absolute without external causation or contingency. G. W. F. Hegel critiqued Spinoza's Absolute as incomplete, affirming it as truth yet insufficient without dialectical development into subject-object unity. In , the Absolute evolved into a self-unfolding totality. (1775–1854) conceived it as the primordial identity of subject and object, grasped via intellectual intuition in works like System of Transcendental Idealism (1800), where nature and freedom emerge from an indifferent ground, with art as the highest revelation of this unity. (1770–1831) systematized it as the Absolute Idea or Spirit, a concrete process of dialectical negation and reconciliation in Phenomenology of Spirit (1807) and (1812–1816), wherein reality realizes itself through historical and logical progression toward self-knowledge, culminating in philosophy as the comprehension of the Absolute. Critiques of the Absolute highlight its speculative abstraction and detachment from sensory evidence. Ludwig Feuerbach (1804–1872), in his 1839 Towards a Critique of Hegel's Philosophy, charged Hegel's version with inverting theology into logic, transforming the human essence into an alien Absolute that subordinates individuals to an illusory whole, thereby masking material anthropology with mysticism. Later, 19th-century materialists and 20th-century analytic philosophers, emphasizing verifiability, rejected it as unfalsifiable; for instance, Schelling himself later critiqued Hegelian absolute idealism (circa 1804–1820) for reducing the Absolute to empty formalism, prioritizing positive philosophy over negative dialectic. These objections underscore the concept's reliance on a priori reasoning over causal-empirical mechanisms, contributing to its marginalization in post-positivist thought.

Absoluteness in theology

In , absoluteness denotes the divine as the self-existent, independent, and that grounds all contingent , free from limitation, composition, or dependence on external factors. This conception emphasizes God's —existence from Himself alone—and immutability, distinguishing the divine from created beings subject to change or . Theistic traditions, particularly monotheistic ones, posit as the Absolute to affirm over the , avoiding pantheistic conflation or relativistic dilution where blends with or yields to finite realities. Central to is the doctrine of , which holds that possesses no metaphysical parts, distinctions between essence and attributes, or internal composition, as any such division would imply or dependence incompatible with absoluteness. Proponents argue that God's being is identical to His attributes—such as , , and holiness—ensuring pure actuality without potentiality or passivity. James Dolezal, in examining this metaphysics, contends that true absoluteness requires simplicity, for a composite would rely on its parts for , undermining self-sufficiency. This view traces to patristic and medieval thinkers but faces in some contemporary Reformed circles for potentially blurring personal distinctions in the , though defenders maintain it preserves relationality within unity. Absoluteness also manifests in God's moral and ontological independence, as articulated in evangelical systematics: God has no beginning or end, constitutes absolute reality itself, depends on nothing, and sustains all else by His will. John Piper outlines this as entailing that every aspect of creation relies on God, while He remains unconditioned, countering anthropocentric remakings of divinity that impose human limits. Holiness exemplifies this, denoting God's infinite moral purity and separation from creaturely imperfection, demanding human recognition of sin's incompatibility without relativizing divine standards. Theological absolutes thus function as non-negotiable truths—such as God's sovereignty and the distortion of human image-bearing by sin—resisting revision to accommodate cultural pluralism, which some sources attribute to institutional pressures favoring inclusivity over scriptural fidelity.

Mathematics

Absolute value

The absolute value of a x, denoted |x|, is defined as x if x \geq 0 and -x if x < 0. This definition captures the geometric distance of x from 0 on the real number line, independent of direction. The function f(x) = |x| produces a V-shaped graph symmetric about the y-axis, with a vertex at the origin. Key properties include non-negativity (|x| \geq 0 for all real x, with equality if and only if x = 0), multiplicativity (|xy| = |x| \cdot |y|), and the triangle inequality (|x + y| \leq |x| + |y|). These follow from the distance interpretation and enable rigorous proofs in analysis, such as deriving the metric on the real line. The notation |x| using vertical bars originated with Karl Weierstrass in 1841, building on earlier uses of "modulus" for magnitudes in complex numbers by Jean-Robert Argand in 1806. In equations and inequalities, absolute values yield piecewise solutions; for instance, |x - a| = b (with b > 0) solves as x = a + b or x = a - b. Applications span defining norms in vector spaces, error bounds in approximations (e.g., |f(x) - L| < \epsilon for limits), and solving systems where magnitude matters over sign, such as in optimization or distance metrics./01:_Functions/1.06:_Absolute_Value_Functions) Generalizations extend to complex numbers as the modulus |z| = \sqrt{a^2 + b^2} for z = a + bi, preserving similar properties for Euclidean norm.

Absolute convergence and advanced concepts

A series \sum_{n=1}^\infty a_n of real or complex numbers converges absolutely if the series of absolute values \sum_{n=1}^\infty |a_n| converges. Absolute convergence is a stricter condition than ordinary convergence, as it ensures the series behaves robustly under rearrangements and other operations. Absolute convergence implies convergence of the original series. Specifically, if \sum |a_n| converges, then \sum a_n converges, a result proven using the triangle inequality: for partial sums s_m = \sum_{k=1}^m a_k and t_m = \sum_{k=1}^m |a_k|, the Cauchy criterion for \sum |a_n| implies |s_p - s_q| \leq |t_p - t_q| for p > q, so \sum a_n is Cauchy and thus convergent in complete spaces like \mathbb{R} or \mathbb{C}. This theorem holds in normed vector spaces, where the norm replaces the absolute value. A hallmark of absolute convergence is invariance under term rearrangement: any permutation of an absolutely convergent series sums to the same value, as the rearranged absolute series \sum |a_{\sigma(n)}| converges to the same limit by the monotone convergence theorem for positive terms. In contrast, conditionally convergent series—those that converge but not absolutely, such as the alternating harmonic series \sum (-1)^{n+1}/n—can sum to arbitrary values under rearrangement, as shown by Riemann's rearrangement theorem. Common tests for absolute convergence include the ratio test and root test. The ratio test states that if L = \lim_{n\to\infty} |a_{n+1}/a_n|, then the series converges absolutely if L < 1 and diverges if L > 1; it is inconclusive if L = 1. The root test uses L = \lim_{n\to\infty} \sqrt{|a_n|}, with the same criteria. These apply directly to \sum |a_n| and are effective for factorials, exponentials, and power series, where the radius of convergence R = 1/L determines absolute convergence inside the interval ( -R, R ). In advanced settings, extends to series of functions and . The provides a criterion for : if |f_n(x)| \leq M_n for all x in a domain and \sum M_n < \infty, then \sum f_n(x) converges absolutely for each x and uniformly on the domain. This test justifies term-by-term differentiation or integration of within the and is pivotal in for ensuring uniform approximation by trigonometric polynomials. In Banach spaces, absolute summability \sum \|x_n\| < \infty implies convergence of \sum x_n, with applications to unconditional convergence in Hilbert spaces.

Physics and Natural Sciences

Absolute zero

Absolute zero is defined as the theoretical lowest temperature, at which the thermal motion of particles in a system reaches its minimum value, corresponding to 0 (K) on the absolute temperature scale. This equates to -273.15 degrees (°C) or approximately -459.67 degrees Fahrenheit (°F), determined through extrapolation of the , where pressure or volume approaches zero as temperature decreases. At this point, a system's approaches a constant minimum, often zero for a perfect crystalline substance, as stated by the third law of thermodynamics, which implies that the number of accessible microstates becomes singular, eliminating disorder. The concept emerged from 19th-century observations of gas behavior under , where volume extrapolates to zero at -273.15°C, prompting William Thomson () to propose an in 1848 based on thermodynamic principles rather than arbitrary fixed points. Earlier insights, such as Robert Boyle's 1665 experiments linking to reduced motion, laid groundwork, but Kelvin's scale formalized the limit by inverting the Carnot efficiency equation, deriving without reliance on specific substances. refines this: even at 0 K, from the Heisenberg sustains residual vibrations, preventing total immobility and ensuring unattainability in finite processes. Reaching absolute zero is impossible in practice, as the third law requires infinite energy extraction stages—each cooling step demands progressively more work for , per the ./11:_The_Third_Law_Absolute_Entropy_and_the_Gibbs_Free_Energy_of_Formation/11.13:_Absolute_Zero_is_Unattainable) Experiments approach it via techniques like adiabatic demagnetization (reaching millikelvins in 1930s) or and evaporative methods, achieving nanokelvin regimes for Bose-Einstein condensates, where atoms collectively occupy the , exhibiting macroscopic quantum coherence. Near these temperatures, phenomena include (zero electrical resistance in materials like mercury below 4.2 K, observed 1911) and (frictionless flow in helium-4 below 2.17 K, 1938), driven by formation and quantum tunneling unhindered by thermal noise. Such low temperatures reveal quantum magnetism and exotic states, like spin liquids where magnetic moments resist ordering due to geometric frustration, probed in ultracold atomic gases. While "negative temperatures" have been engineered in isolated spin systems (effectively hotter than positive infinity via ), they do not violate the limit but represent non-equilibrium entropy decrease, inapplicable to . These pursuits, from dilution refrigerators to space-based labs like NASA's Cold Atom Lab (operational since 2018, producing clouds at microkelvins), underscore absolute zero's role as a boundary for probing fundamental quantum-thermal interplay.

Absolute temperature scale

The absolute temperature scale, also known as the scale, sets zero at —the theoretically lowest temperature at which the thermal motion of particles in a substance ceases, corresponding to a complete absence of in classical . This scale provides a measure independent of any particular substance's phase changes, enabling direct proportionality between temperature and quantities like pressure-volume products in ideal gases or changes in reversible processes. Unlike interval scales such as or , which allow negative values and are anchored to empirical points like water's freezing, the absolute scale ensures positive values throughout and facilitates ratio-based calculations fundamental to the . William Thomson, later , proposed the scale in 1848 through his paper "On an Absolute Thermometric Scale founded on Carnot's Principle of the Motive Power of Heat," deriving it from Sadi Carnot's work on heat engines and the efficiency of reversible cycles. Thomson reasoned that the scale's zero must align with the point where no heat can be extracted from a body, extrapolating from air data to place at approximately -273°C on the scale. This thermodynamic foundation avoided reliance on material-specific properties, contrasting with earlier scales, and established as a measure of average molecular per degree of freedom, as later formalized in the . The unit of this scale, the (K), was formalized in the (SI). Prior to the 2019 redefinition, one kelvin was defined as 1/273.16 of the at 's —the unique state where solid, liquid, and vapor phases coexist at 0.01°C and 611.657 pressure—yielding exactly 273.16 K for that point. The current definition fixes the at exactly 1.380649 × 10^{-23} J/K, linking the kelvin directly to and allowing realization via thermometry or other methods without reference to water, while preserving the scale's continuity with prior measurements. Conversion from follows T(K) = T(°C) + 273.15, with at 0 K or -273.15°C. In physics and engineering, the is essential for applications where negative temperatures would distort physical laws, such as the (PV = nRT), (Stefan-Boltzmann law, proportional to T^4), or quantum statistics in Bose-Einstein condensates near . It underpins thermodynamic efficiency calculations, where ratios like T_hot / T_cold determine limits, and supports precise measurements in fields like , where temperatures below 1 K are achieved using dilution refrigerators or . Empirical verification through experiments, such as extensions to low pressures, confirms the scale's validity down to near-absolute zero, though quantum effects introduce deviations from classical predictions at extreme lows.

Absolute space and time

In Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687), form the foundational framework for , posited as independent entities existing without reference to material bodies or observers. Newton defined absolute space as remaining "always similar and immovable" in its own nature, irrespective of external relations, contrasting it with relative space, which is a measurable derived from sensible objects like ships or rooms. Absolute time, similarly, "flows equably without relation to anything external," termed duration, distinct from relative time measured by motions such as planetary orbits or clock ticks, which may vary unequally. These concepts enabled Newton to distinguish true motion—alteration of position in absolute space—from apparent motion, grounding his three laws of motion in an unobservable but necessary absolute reference for inertial frames and forces like centrifugal in rotating systems. Newton defended absolute space and time through thought experiments, such as the rotating : water in a bucket spun relative to surrounding bodies climbs the walls due to absolute against fixed , evidenced by concave surface and inertial effects, not merely relative to the water itself. This argument, detailed in the Scholium to the Definitions, countered relational views by asserting that rotational dynamics require an absolute frame to explain non-relativistic inertial forces, as relative motions alone fail to account for observed deviations from uniform straight-line paths. Philosophically, viewed as God's —an immaterial medium for divine —while time's uniformity ensured causal consistency across the universe, independent of local events or velocities. Critiques emerged contemporaneously from relationalists like Gottfried Wilhelm Leibniz, who argued space and time as mere orders of coexistences and successions among bodies, rendering absolute versions metaphysically superfluous and undetectable empirically. Ernst Mach later (1883) proposed inertia derives from acceleration relative to distant stars, challenging absolute space by suggesting no privileged frame exists without cosmic matter distribution. Experimental evidence mounted against Newton's absolutes: the 1887 Michelson-Morley experiment yielded null results for Earth's motion through a hypothesized luminiferous aether, implying no detectable absolute rest frame for light propagation at constant speed c ≈ 299,792 km/s. Albert Einstein's (1905) integrated space and time into , where simultaneity, length, and duration contract with relative velocity, abolishing absolute frames and aligning with electromagnetic invariance. (1915) further geometrized as spacetime curvature by mass-energy, confirming relational dynamics through tests like the 1919 Eddington eclipse observation of starlight deflection by the Sun's field, matching predictions to within 20% error. , including and cosmology, operates without absolute space or time; GPS satellites adjust clocks for relativistic effects, with verified to parts per billion, underscoring empirical rejection of Newtonian absolutes in favor of observer-dependent metrics. While some approaches explore absolute-like elements (e.g., fixed background in certain formulations), no empirical restoration of Newton's framework has occurred, as relational accounts for observations from particle accelerators to galactic rotations.

Absolute pitch

Absolute pitch, also known as perfect pitch, is the cognitive ability to identify or produce a given without an external reference . This trait enables individuals to name the (e.g., C, D-sharp) of an isolated note or recreate a specified accurately, distinguishing it from , which relies on comparisons between tones. Possession of often correlates with enhanced auditory memory and tonal language backgrounds, where prevalence is higher among speakers of languages like or due to lexical systems reinforcing pitch categorization in early development. The prevalence of in the general is estimated at approximately 0.01%, or 1 in 10,000 individuals, though rates vary by demographic factors such as musical and . Among professional musicians, incidence rises to 10-15%, suggesting a between innate predispositions and environmental exposure. Genetic studies indicate , with showing phenotypic overlap with traits like and shared genetic loci identified in genome-wide association scans of musically trained cohorts. Twin studies further support a polygenic basis, estimating around 70-80% when controlling for shared musical upbringing. Debate persists on whether is primarily innate or acquired, with evidence pointing to a in for optimal development. Longitudinal data from musically trained children demonstrate that onset of formal before age 6 correlates strongly with acquisition, aligning with windows where labeling becomes encoded without conscious effort. However, recent experimental interventions challenge strict innateness claims: adults without prior , using targeted protocols—such as repeated tone identification with adaptive difficulty—achieved identification accuracies exceeding 80% for isolated pitches after 20-30 hours of , persisting months post-intervention. These findings suggest that while genetic and early environmental factors predispose individuals, aspects of processing remain malleable in adulthood, potentially through of auditory-reference associations rather than innate hardwiring. Critically, such yields pseudo-absolute pitch, which may degrade without maintenance, unlike the effortless recall in congenital cases. Neurologically, engages heightened activation in the left and , regions implicated in auditory processing and , as revealed by fMRI studies comparing possessors and non-possessors. This specialization may arise from early pitch-to-label mapping, reducing reliance on relational processing dominant in . Testing protocols typically involve randomized presentation of 30-60 isolated tones across octaves, scoring accuracy above 85% as indicative of , though variability exists in threshold definitions and exclusion of pseudo-pitch effects. In musical practice, facilitates transcription, , and but can hinder in equal-tempered systems or induce interference in non-standard tunings. Empirical assessments confirm no universal cognitive superiority beyond pitch tasks, underscoring it as a domain-specific perceptual enhancement rather than general marker.

Politics and Law

Absolute monarchy

An is a governmental system in which a hereditary exercises unrestricted autocratic over the , unbound by constitutions, legislatures, or other institutional checks, often justified by doctrines such as the . This form contrasts with constitutional monarchies, where the ruler's powers are limited by law or representative bodies, and emerged prominently in during the 16th to 18th centuries amid efforts to centralize fragmented feudal following medieval disruptions like invasions and civil strife. Key characteristics include the monarch's direct control over legislation, taxation, military command, and religious policy, with often subordinated through centralization or bureaucratic expansion to prevent rival power centers. Historically, absolute monarchy reached its zenith in under (reigned 1643–1715), who centralized power by revoking noble privileges, building the Palace of Versailles as a tool to monitor and co-opt the , and declaring "" to embody the state's indivisibility with his person. His policies, including the in 1685 revoking Protestant rights, enforced religious uniformity under Catholicism, while mercantilist reforms under ministers like expanded state revenue through monopolies and infrastructure, funding wars that strained but did not immediately collapse the system. Similar absolutism appeared in Russia under (reigned 1682–1725), who modernized the military and bureaucracy via Western imports, subjugating the boyars and expanding territory through conquests like the (1700–1721). In the and Mughal India, sultans and emperors wielded comparable unchecked power until internal decays and European pressures eroded it by the . The doctrine underpinning often invoked divine right, positing the ruler as God's appointed agent accountable only to divine judgment, which rationalized suppression of dissent and justified expansionist policies. This system fostered administrative efficiency in capable hands, enabling rapid state-building, but inherent risks included succession crises, fiscal overreach from perpetual warfare, and elite resentment, as seen in France's mounting debts from XIV's conflicts like the (1701–1714). In the modern era, absolute monarchies persist in fewer states, primarily resource-rich Gulf principalities and isolated theocracies, where rulers maintain control via oil revenues, tribal alliances, and suppression of opposition rather than broad popular consent. Examples include , where King Salman bin Abdulaziz (ascended 2015) holds veto-proof authority over policy despite a consultative assembly; , under Hassanal Bolkiah (reigned since 1967), who controls a -based system with personal wealth from exceeding $20 billion; and , led by (since 2020), who inherits absolute legislative and judicial powers. The operates as an elective absolute monarchy under the , with (elected 2013) exercising supreme executive, legislative, and judicial authority over its 800 residents. These regimes demonstrate viability in low-population, high-wealth contexts but face challenges from , demands for reform, and external sanctions, as evidenced by Brunei's 2019 code expansions sparking international boycotts. The decline of absolute monarchy in Europe stemmed from Enlightenment critiques of arbitrary rule—thinkers like John Locke (1632–1704) argued for consent-based government in Two Treatises of Government (1689)—coupled with fiscal crises, as rulers' wars outpaced revenue without parliamentary taxation, precipitating events like the Glorious Revolution (1688) in England and the French Revolution (1789). Empirical patterns show absolutism's unsustainability in agrarian economies reliant on noble cooperation, where unchecked power invited revolts or coups, whereas modern survivals correlate with hydrocarbon rents insulating rulers from taxpayer revolts. Sources on this decline, often from Western academic traditions, may underemphasize absolutism's stabilizing role in pre-modern chaos while amplifying narratives of inevitable progress toward democracy, yet causal evidence links its erosion to specific triggers like debt defaults and ideological shifts rather than inherent moral flaws.

Absolute sovereignty and power

Absolute sovereignty denotes the supreme, indivisible, and unrestricted authority of a political entity, such as a or its , unbound by external or internal constraints like superior laws or divided powers. This concept, central to early modern political theory, posits that the sovereign holds perpetual power to legislate, judge, and enforce without needing consent from subordinates or yielding to any higher authority. formalized it in his 1576 work Les Six Livres de la République, defining as "the absolute and perpetual power of a commonwealth," emphasizing its indivisibility to prevent civil discord. Thomas Hobbes extended this in Leviathan (1651), arguing that absolute emerges from a where individuals surrender rights to a unified to escape the anarchic "," characterized by . For Hobbes, the sovereign's power must be absolute—extending to all matters within the territory, including life and death decisions—to maintain peace, as any limitation invites interpretive disputes and conflict. He distinguished this from tyranny by noting the sovereign's self-interest aligns with subjects' security, though critics contend it risks unchecked abuse absent mechanisms like divided powers. Absolute power, as the exercise of this sovereignty, manifests in the sovereign's capacity to override positive laws, declare , impose taxes, and absolve subjects from obligations, provided it adheres to natural or in theorists like Bodin. Historically, this underpinned centralized states post-Westphalia (), where rulers claimed independence from imperial or papal oversight, though practical absoluteness eroded with and international norms. In Bodin's framework, even absolute rulers remain theoretically bound by God's commandments, such as prohibiting unjust killing, to legitimize their authority as divine representatives. Modern interpretations, however, highlight tensions: while no state achieves pure absoluteness amid global interdependence, the doctrine persists in justifying non-intervention and unilateral actions.

Music and Arts

Absolute music

Absolute music denotes instrumental compositions designed to be experienced and evaluated on the basis of their internal sonic organization, formal coherence, and structural logic, independent of any intent to represent or evoke specific external narratives, images, scenes, or emotions. This approach privileges music's autonomy as an form, deriving meaning from elements such as , , , and rather than programmatic associations. In distinction to , which employs motifs or developments to illustrate literary, pictorial, or dramatic content, absolute music rejects such representational aims, asserting that its essence lies in self-contained "tonally moving form." The concept traces its philosophical roots to late 18th-century German Romantic thinkers, who elevated instrumental music's abstract spirituality over vocal or descriptive forms, viewing it as a direct conduit to the ineffable. The term "" was coined by in 1846 to characterize non-programmatic instrumental repertory, though Wagner critiqued it as limited and himself pursued integrated music-drama fusing music with text and action. advanced the idea decisively in his 1854 treatise Vom Musikalisch-Schönen (On the Musically Beautiful), arguing that music's content inheres in its formal patterns and logical progression, not in the subjective imputation of particular feelings or ideas, which he deemed illusory and unverifiable. This advocacy fueled the mid-19th-century "," a polarized debate in German musical circles over aesthetic priorities, where 's formal purity clashed with programmatic experimentation. Proponents like Hanslick and composer defended as the pinnacle of artistic integrity, upholding classical genres such as the and as vehicles for universal expression unbound by anecdote. Opponents, including and Wagner, promoted program music's capacity to convey philosophical or narrative depth through symphonic poems and leitmotifs, viewing as aridly abstract. The controversy, peaking around 1850–1860 in periodicals and concert programming, reflected broader tensions between tradition and innovation in , with often aligned with conservative . Exemplary works include Brahms's symphonies (e.g., ), which prioritize thematic development and motivic unity without explicit titles or descriptions; Mendelssohn's concert overtures and string quartets, emphasizing structural elegance; and Beethoven's late string quartets (e.g., Op. 131, 1826), lauded for their intricate and self-referential depth. Earlier precedents abound in Mozart's symphonies and Bach's fugues, where musical logic prevails over depiction, though the explicit absolute-program crystallized in the . In contemporary practice, much orchestral and continues this tradition, valuing interpretive freedom derived from the score's inherent architecture over imposed narratives.

Works titled "Absolute"

"Absolute" is a single by the British band , released on May 29, 1984, by as the eighth single from their album . Written by frontman , the track features a arrangement with prominent percussion and was noted for its energetic mix by . The Absolute (original Spanish title Lo Absoluto) is a 2022 historical novel by Argentine author Daniel Guebel, translated into English and published by . The work spans six generations of the fictional Deliuskin-Scriabin family, drawing on the lives of composers and to explore themes of genius, madness, memory, music, and family dynamics. Absolute is a 2016 electronic music album by the artist M23, released under the Abstract Mechanisms label and available on Bandcamp. It includes tracks such as "Absolute," "Absolute II," and remixes, blending techno and experimental elements.

Companies and Brands

Absolute Vodka

Absolut Vodka is a premium brand of vodka produced exclusively in Åhus, a village in southern Sweden, using winter wheat and water sourced from the local region. The brand originated in 1879 when entrepreneur Lars Olsson Smith developed a continuous distillation process to create "Absolut Rent Brännvin," meaning "absolutely pure vodka," aiming for higher purity without additives like sugar. This method, still employed today, involves multiple distillations in a single column still, producing a neutral spirit at 40% alcohol by volume. The distillery in Åhus, established in 1906, has an annual production capacity of approximately 100 million liters. Following government of spirit production in , the brand operated under state-owned Vin & Sprit with limited domestic success until its international export began in 1979. The 1979 U.S. launch, marketed with iconic minimalist bottle design and creative advertising campaigns featuring artists like , propelled it to global prominence as one of the top-selling premium vodkas. By emphasizing its origin and purity, Absolut differentiated itself in competitive markets, achieving widespread recognition through flavored variants and limited-edition bottles. In 2008, French multinational acquired Vin & Sprit for 5.63 billion euros, integrating Absolut into its portfolio as the sixth-largest spirits brand worldwide and the leading premium . Under , production remains centered in Åhus, with ongoing innovations in sustainable sourcing—such as for —and expanded flavor profiles like and Mandrin, while maintaining the core unflavored expression. The brand's marketing continues to focus on cultural collaborations and premium positioning, contributing to 's spirits sales despite market fluctuations.

Absolute Software and technology firms

Absolute Software Corporation is a cybersecurity firm specializing in endpoint resilience and zero trust security solutions, enabling organizations to secure devices, data, and users against threats such as and data breaches. Founded in 1993 in , , the company initially developed a platform for tracking, managing, and tracing computers primarily for the education sector. By the early , it expanded partnerships with device manufacturers, embedding its Persistence technology into to ensure always-on connectivity and security even if devices are wiped or OS is removed. This firmware-based approach distinguishes Absolute's offerings, with the technology integrated into over 600 million devices from partners including , , , and . The firm's core products include Absolute Visibility for endpoint insights, Absolute Control for remote and , and Absolute Resilience for automated response and , often deployed as a subscription . These solutions support IT , , and cyber hygiene, with features like geofencing, tamper-proof logging, and self-healing capabilities. Absolute has been recognized for its role in , partnering with more than 28 leading device OEMs to provide factory-embedded . In July 2023, the company was acquired by an affiliate of Crosspoint Capital Partners for approximately $870 million, transitioning to a private entity to focus on scaling its cyber platform. Other technology firms bearing the "Absolute" name include Absolute Technologies, Inc., which develops governance, risk, and compliance (GRC) software solutions for E-Business Suite, emphasizing user access controls automation and revenue visibility. Absolute Technology Solutions, based in , provides managed IT services, , , and , serving local businesses with infrastructure support. These entities operate in narrower niches compared to Absolute Software's global focus.

Other commercial entities

Absolut Bank, officially known as Public Joint Stock Company Absolut Bank, is a commercial bank headquartered in , offering services including lending, deposits, financing, and settlement operations. Founded in 1992, it ranks among Russia's top 25 banks by asset size, with over 3,500 employees and a focus on high-tech development in priority sectors like banking in and St. Petersburg regions. Absolute Radio is a British commercial radio network owned by Bauer Media Audio UK, broadcasting digital stations featuring music from various eras, including Absolute Radio 60s, 80s, and Country variants. Launched in 2008 as a rebrand of Virgin Radio, it faced trademark infringement lawsuits from Absolut Vodka's owner due to name similarity but settled the disputes. Absolute Antibody Ltd. is a UK-based firm founded in 2012 in , specializing in recombinant sequencing, , and production for and diagnostics markets. The company provides royalty-free custom services and a catalog of engineered antibodies, emphasizing reproducibility over traditional hybridoma-derived options, and was acquired by Vector Laboratories in May 2024.

Other Uses

Absolute alcohol and chemistry

Absolute alcohol, also termed anhydrous , is a grade of (C₂H₅OH) dehydrated to contain less than 1% by volume, typically achieving 99.5% to 99.9% purity depending on the production grade. This distinguishes it from rectified or commercial , which forms an with at 95.6% concentration, limiting simple yields. Chemically, it retains 's properties as a colorless, volatile, with a of 78.37°C and of 0.789 g/cm³ at 20°C, but its low content prevents or side reactions in moisture-sensitive processes. Due to its hygroscopic nature, absolute rapidly absorbs atmospheric , requiring sealed storage over desiccants to maintain conditions. Production begins with fermentation of sugars by to yield a dilute solution, followed by to concentrate it to the 95.6% . Further dehydration employs methods such as with entrainers like to shift the vapor-liquid and remove residual , or adsorption using molecular sieves (zeolites) with pore sizes selective for molecules (approximately 0.3 nm). Alternative techniques include reactive distillation with or , achieving contents as low as 0.005% in grades. These processes ensure the absence of , which would otherwise form constant-boiling mixtures resistant to further purification by alone. In , absolute alcohol serves primarily as an solvent for reactions intolerant to trace water, such as the preparation of Grignard reagents (e.g., CH₃MgBr from methyl iodide and magnesium), where water hydrolyzes the organometallic intermediate to yield alkanes and magnesium salts. It facilitates the generation of (NaOEt) by reaction with sodium metal, a strong base used in Claisen condensations and eliminations, as residual water would protonate the . Additionally, it acts as a medium for esterifications under Dean-Stark conditions or extractions requiring non-aqueous polarity, and as a mobile phase carrier in to avoid peak broadening from water interference. Its role extends to , where water-free samples prevent overlapping O-H absorption bands in or NMR analyses.

Absolute dating in sciences

Absolute dating methods in geology, archaeology, and related sciences provide numerical ages for rocks, fossils, artifacts, and geological events by measuring physical properties such as radioactive decay products or annual growth layers, yielding results in calendar years or years before present (BP). Unlike relative dating, which establishes sequence through superposition or stratigraphy, absolute dating assigns specific time values, enabling precise chronologies for events like human migrations or tectonic shifts. These techniques rely on empirical measurements calibrated against known standards, with applications spanning from recent millennia to billions of years ago. The foundational principle of many absolute dating methods is radiometric dating, which exploits the predictable decay of unstable isotopes into stable daughters at constant rates, characterized by half-lives independent of environmental conditions. For instance, the ratio of parent to daughter isotopes in a closed system, such as a mineral crystal, allows calculation of elapsed time since the system's formation or last heating event, assuming no initial daughter isotopes or loss/gain post-closure. Corrections for atmospheric variations or contamination enhance reliability, as in calibration curves derived from tree rings or corals. Limitations include the need for suitable materials (e.g., organic for short-lived isotopes) and potential open-system behavior from weathering, addressed through isochron plots or concordia diagrams for verification. Prominent techniques include , applicable to organic remains up to about 50,000 years old via the decay of ( 5,730 years), where post-mortem cessation of atmospheric C-14 uptake leads to measurable decline; accuracy reaches ±20-50 years for recent samples after calibration against records. Potassium-argon (K-Ar) dating targets volcanic minerals like sanidine, measuring argon-40 from decay ( 1.25 billion years), suitable for dates exceeding 100,000 years to 4 billion, as argon accumulates in solidified lava without escape. Uranium-lead (U-Pb) dating of crystals employs dual decay chains (U-238 to Pb-206, 4.47 billion years; U-235 to Pb-207, 704 million years), providing robust ages up to Earth's formation via concordant ratios, with precisions of 0.1-1% for ancient rocks. Non-radiometric methods, such as counting annual tree rings cross-matched to master sequences or optically stimulated measuring trapped electrons in sediments last exposed to , complement these for contexts.

Linguistic and everyday usage

The English word absolute entered the language in the late , derived from Latin absolutus, the past participle of absolvere, meaning "to set free," "to complete," or "to detach." This etymological root conveys notions of unrestricted or from external conditions, influencing its core semantic range across linguistic and philosophical contexts. In grammatical usage, absolute describes constructions that stand independently from standard syntactic relations within a sentence. An absolute phrase, for instance, consists of a noun or pronoun paired with a participle and modifiers, functioning to modify the entire clause rather than a specific element; examples include "weather permitting" in "We proceed, weather permitting" or "his tail wagging" in "The dog approached, his tail wagging." Such phrases add supplementary detail without integrating as subjects or objects, a feature noted in English syntax since at least the 19th century. Additionally, absolute adjectives or possessives operate without qualifiers, as in "the absolute truth" or "absolute possession," emphasizing unqualified states. In everyday usage, absolute primarily serves as an indicating totality, , or from doubt or mixture, such as "absolute silence" for complete quiet or "absolute monarchy" for rule without constitutional limits. It often intensifies expressions colloquially, as in "absolute joy" or "absolute ," conveying extremity without literal , a pattern evident in spoken and written English corpora from the onward. This intensifier role has grown prevalent in informal contexts, though it retains formal connotations of purity or certainty, like "absolute alcohol" for undiluted . Claims of "absolute truth" invoke its philosophical undertone of unchanging , contrasting with relative qualifiers, but everyday applications rarely demand rigorous beyond rhetorical emphasis.