Fact-checked by Grok 2 weeks ago

Element

Element is a free and open-source client application for the Matrix protocol, designed for secure, decentralized real-time communication including end-to-end encrypted text messaging, voice calls, video conferencing, and collaborative tools. It emphasizes user control through federation across independent servers, enabling self-hosting and interoperability without reliance on centralized providers, which distinguishes it from proprietary alternatives. Originally launched as Riot.im in 2016 and later rebranded from Vector, Element has been developed by the creators of the Matrix standard to prioritize digital sovereignty, privacy, and extensibility for both individual users and large-scale enterprise deployments. Notable for its cross-platform availability on web, desktop, and mobile, the software supports features like spaces for organized group interactions and integrations with third-party bridges to legacy networks, fostering resilient communication infrastructures resistant to single points of failure or censorship. While praised for advancing open standards in an era dominated by closed ecosystems, Element's adoption has been driven by privacy advocates, open-source communities, and institutions requiring verifiable security over vendor lock-in.

Etymology and Core Concepts

Linguistic origins

The English word element derives from element, denoting fundamental constituents of the world or celestial bodies, borrowed from element. This term, in turn, stems directly from Latin elementum, which signified "a , rudiment, or basic component" and served as a for the Greek stoicheîon (στοιχεῖον), meaning "one of a series" or a primary constituent in philosophical contexts such as the building blocks of matter. The Latin elementum first appears in texts around the 3rd century BCE in works by authors like , where it described indivisible principles akin to atoms or letters of the , reflecting influences from Epicurean and thought. The precise etymology of Latin elementum remains uncertain, with no consensus among linguists on its root formation; proposed derivations include a compound from ele- (possibly akin to el-, relating to origins or emergence) and -mentum (a suffix denoting instrument or product), or a connection to the sequence of letters L-M-N in the alphabet, as elementa could refer to basic letters or rudiments in early education. Less supported theories link it to verbs like alo ("to nourish" or "sustain"), implying elements as sustaining principles, though this lacks direct philological evidence. By the late Roman period, elementum had extended to denote the classical four elements—earth, air, fire, and water—as articulated by Empedocles and systematized by Aristotle, influencing its semantic shift toward natural and cosmic fundamentals. In English, the term entered usage by the , initially in theological and alchemical writings to describe essential principles or sacraments, before broadening in scientific discourse during the to encompass chemical substances. This evolution preserved the core connotation of simplicity and primacy, distinguishing element from related terms like principium (principle) by emphasizing indivisibility and foundational status. Modern lexicographical analyses, such as those in the , underscore the term's persistence in denoting irreducible components across , , and , without alteration in its Indo-European lineage.

Fundamental definitions across disciplines

In philosophy, an element is conceptualized as a primary, indivisible constituent from which composite entities are formed, incapable of further division into another form without altering its essential nature. Aristotle articulated this in his Metaphysics, stating: "That from which something is composed, as a primary constituent that is in form indivisible into another form, is called an element," with examples including letters as elements of syllables or the four classical substances (earth, air, fire, water) as elements of physical bodies. In , an element is defined as a of atoms—or a pure substance—wherein all atoms share the identical number of protons in their nuclei, corresponding to a unique . This definition, formalized by the International Union of Pure and Applied Chemistry (IUPAC), underscores the indivisibility of elements by chemical means into simpler substances, distinguishing them from compounds. In mathematics, particularly , an element denotes a distinct object or member belonging to a set, which is a well-determined collection of such objects; sets themselves may serve as elements of other sets. This foundational notion, primitive in axiomatic frameworks like Zermelo-Fraenkel set theory, enables the construction of mathematical structures without presupposing further decomposition of elements. In physics, fundamental elements are identified as elementary particles, defined as subatomic entities not composed of other particles, serving as the basic building blocks of matter and forces within the . These include quarks, leptons, and gauge bosons, with their indivisibility verified through high-energy experiments excluding observable substructure as of 2023.

Philosophy and Religion

Ancient elemental theories

Pre-Socratic philosophers in sought a single arche (originating principle) underlying the cosmos, marking an early shift toward naturalistic explanations of matter. , active circa 585 BCE, identified water as the fundamental substance, arguing it could transform into other forms through processes like and , based on observations of moisture's ubiquity in life and nature. His student , around 546 BCE, proposed the apeiron—an eternal, indefinite, and boundless material—as the source to avoid privileging one observable substance, positing it generates opposites like hot and cold through separation. , circa 546–528 BCE, refined this by naming air as the primary element, compressible into denser forms like wind, cloud, water, earth, and fire. of , active around 500 BCE, elevated fire as the arche, emphasizing its transformative and unifying role in perpetual flux, where "all things are an exchange for fire, and fire for all things, like goods for gold and gold for goods." Empedocles of Acragas, circa 495–435 BCE, advanced a pluralistic theory by introducing four eternal "roots" (rhizomata)—earth, water, air, and fire—as the indivisible building blocks of matter, combined and separated by cosmic forces of (attraction and unity) and Strife (repulsion and division). This framework explained change without invoking a single mutable principle, positing cycles of cosmic unification and fragmentation; for instance, gathers the roots into a spherical god-like unity, while Strife disperses them into diversity, including living beings formed by elemental mixtures. later credited as the first to clearly articulate these four material elements, though he critiqued the theory for lacking qualitative distinctions. Aristotle, in works like On Generation and Corruption circa 350 BCE, systematized the four elements into a comprehensive framework, assigning each paired opposites: fire (hot and dry), air (hot and moist), water (cold and moist), and earth (cold and dry). These qualities enabled transmutation—e.g., heating water (cold-moist) yields air (hot-moist)—while natural places dictated motion: earth and water toward the center, fire and air outward. He introduced a fifth element, aether (quintessence), incorruptible and circularly moving, composing the celestial spheres beyond the sublunary realm of changing elements. This theory dominated Western cosmology for over two millennia, influencing alchemy and medieval science by providing a causal mechanism for mixture and change rooted in observable properties rather than mere aggregation. Parallel elemental schemes emerged independently in other ancient civilizations. In Indian philosophy, the pancha mahabhuta (five great elements)—earth (prithvi), water (ap), fire (agni), air (vayu), and space (akasha)—appear in Vedic texts like the Upanishads (circa 800–500 BCE) and Samkhya school, where they constitute gross matter (sthula bhuta) from subtler tanmatras, emphasizing hierarchical evolution from subtle to manifest without strict transformative cycles. Chinese cosmology developed wuxing (five phases)—wood, fire, earth, metal, water—during the Spring and Autumn Period (770–476 BCE), not as static substances but dynamic processes governing interactions via generation (e.g., wood fuels fire) and conquest (e.g., water extinguishes fire), applied to politics, medicine, and seasons rather than fundamental particles. These non-Greek systems prioritized relational cycles over qualitative mixtures, reflecting cultural emphases on harmony and change absent in Aristotelian permanence.

Religious and symbolic uses

In , which influenced subsequent religious traditions, the four classical elements—earth, , air, and fire—were conceptualized by around 450 BCE as fundamental building blocks of the , each associated with qualities like hot, cold, wet, and dry, and linked to divine forces or gods. These elements symbolized stability (), fluidity (), intellect (air), and transformation (fire), appearing in religious rituals such as Pythagorean mysticism, where they represented cosmic harmony and were invoked in purification rites. In Hellenistic and Roman religions, the elements extended to symbolic correspondences with the four humors (black bile for earth, for water, for air, yellow bile for ), underpinning medical and divinatory practices in texts like those of (c. 400 BCE), where imbalances were seen as causes of illness requiring ritual balancing through offerings or elemental meditations. The Stoics, including (c. 300 BCE), integrated elements into a pantheistic , viewing as the primal element from which others derived, symbolizing divine or reason permeating the universe. Hinduism's Pancha Mahabhuta framework, outlined in texts like the (c. 800–200 BCE), posits five elements—earth (), water (), fire (), air (), and ether ()—as manifestations of , the , with symbolic roles in and for balancing doshas and achieving spiritual enlightenment through practices like (breath control for air) or (fire rituals). Ether, as the subtlest element, symbolized infinite space and consciousness, influencing temple architecture where elements were spatially arranged to mirror cosmic order. Chinese Taoism and cosmology feature the Wu Xing (five phases)—wood, fire, earth, metal, and water—dating to the (475–221 BCE), not as static substances but dynamic processes symbolizing cyclical change and harmony, used in religious divination, , and rituals to align human actions with natural forces, as detailed in the (c. 139 BCE). These phases governed sacrificial offerings and imperial ceremonies, with imbalances believed to provoke ancestral spirits or cosmic disharmony. In Western esoteric traditions, including medieval and , elements served as archetypes for spiritual transmutation, with (1493–1541) expanding them to include (earthly body), (soul), and mercury (spirit), symbolizing the philosopher's stone's creation through elemental purification rituals. Such symbolism persisted in and , where elements represented moral virtues—earth for temperance, fire for fortitude—invoked in initiatory rites for personal enlightenment, though these frameworks lack empirical validation and reflect pre-modern analogical reasoning rather than causal mechanisms. Modern neopagan movements, like (formalized by in 1954), ritually invoke elements in quartered circles for protection and manifestation, drawing from these historical precedents but adapted without scientific substantiation.

Empirical critiques and supersession by science

Empirical investigations beginning in the 17th century exposed fundamental flaws in the classical theory of four elements—earth, water, air, and fire—as proposed by Empedocles around 450 BCE and systematized by Aristotle in the 4th century BCE. These elements were posited as indivisible substances combining through qualitative changes to form all matter, but lacked quantitative experimental validation, relying instead on observational analogies without controlled testing. Robert Boyle's The Sceptical Chymist (1661) provided one of the earliest rigorous critiques, arguing through experimental demonstrations that the four elements failed to account for chemical compositions and decompositions, such as the variability in "air" and "fire" across substances. Boyle advocated a corpuscular (proto-atomic) view, emphasizing that true elements must be identified via repeatable mechanical experiments rather than philosophical deduction, thus undermining the Aristotelian framework's explanatory power. By the 18th century, Antoine Lavoisier's quantitative experiments further dismantled elemental theories, including successors like phlogiston, which retained fire-like principles akin to ancient fire. Lavoisier's precise measurements of mass conservation in reactions, detailed in his 1789 Traité élémentaire de chimie, showed water as a compound of and oxygen rather than a primordial element, directly refuting its status in classical schemes. He identified 33 substances as provisional elements based on failure to decompose further via and gravimetric methods, shifting chemistry toward empirical verifiability over speculative qualities like hot/cold or wet/dry. The advent of in John Dalton's 1808 A New System of Chemical Philosophy completed the supersession, positing of distinct elements combining in fixed ratios, supported by laws of definite and multiple proportions derived from analytical data on gases and salts. This framework, refined by Dmitri Mendeleev's 1869 periodic table organizing 63 known elements by atomic weight and properties, revealed patterns inexplicable by four-element theory, such as recurring chemical behaviors across hundreds of substances. Modern science, grounded in , , and particle accelerators, confirms over 118 elements as fundamental building blocks, each with unique nuclear and electronic structures, rendering ancient elemental models obsolete for causal explanations of matter.

Natural Sciences

Chemical elements

A is a pure substance composed of atoms that all possess the same , defined as the number of protons in the of those atoms. This uniquely identifies the element and determines its position in the periodic table, where elements are arranged in order of increasing to reveal recurring patterns in chemical and physical properties, such as , , and reactivity. The periodic table currently lists 118 confirmed elements, ranging from (atomic number 1) to (118), with no new elements officially recognized as of 2025. Elements are broadly classified into metals (e.g., iron, ), which typically exhibit luster, malleability, and conductivity; nonmetals (e.g., oxygen, ), which are often gases or brittle solids with poor conductivity; and metalloids (e.g., , ), displaying intermediate properties. Approximately 94 elements occur naturally on , primarily through primordial in stars and subsequent cosmic processes, while the remaining 24 (from , atomic number 93, onward) are synthetic, created via particle accelerators and nuclear reactors and exhibiting extreme instability with half-lives often measured in seconds. (43) and (61) are exceptions among lighter elements, as they have no stable isotopes and occur only in trace amounts from or , rendering them effectively synthetic for practical purposes. In , elemental abundances reflect geological processes like and , with oxygen dominating due to its role in and oxides. The table below summarizes the most abundant elements by mass percentage:
ElementSymbolAbundance (% by weight)
OxygenO46.6
Si27.7
AluminumAl8.1
IronFe5.0
CalciumCa3.6
SodiumNa2.8
K2.6
MagnesiumMg2.1
Chemically, elements cannot be decomposed into simpler substances by chemical means but can form compounds through or sharing, governed by electrons in outer shells, which align with periodic table groups. Isotopes, variants with differing counts but identical proton numbers, minimally affect chemical behavior due to near-identical electron configurations, though they influence nuclear stability and applications like . Synthetic elements, lacking natural abundance, enable studies of relativistic effects and superheavy nuclei, advancing despite their fleeting existence.

Physical components

Chemical elements are constituted by atoms, the fundamental units sharing identical atomic numbers, defined as the count of protons in the atomic nucleus. Protons, positively charged subatomic particles with a mass of approximately 1.6726 × 10^{-27} kg, reside in the nucleus alongside neutrons, which are electrically neutral particles of similar mass (about 1.6749 × 10^{-27} kg) that contribute to nuclear stability via the strong nuclear force. The nucleus, comprising protons and neutrons (collectively nucleons), occupies a minuscule volume—roughly 10^{-15} meters in diameter—while the overall atomic radius spans about 10^{-10} meters, rendering most of the atom empty space. Electrons, negatively charged particles with negligible mass (9.1094 × 10^{-31} kg), orbit the in probabilistic electron clouds or shells governed by , balancing the positive nuclear charge in atoms. The number of electrons in a atom equals the number of protons, determining chemical reactivity through valence electrons in outer shells. Variations in neutron count yield isotopes: of the same element (fixed protons) but differing mass numbers (protons + s), such as hydrogen-1 (protium, no neutrons) and hydrogen-2 (, one ), which exhibit near-identical chemical properties but distinct nuclear stabilities and physical masses. Stable elements typically feature balanced proton-neutron ratios, with lighter elements (e.g., up to calcium-40) approximating 1:1 and heavier ones requiring more neutrons for stability against electrostatic repulsion; beyond , all known isotopes are radioactive, decaying via processes like alpha emission. Synthetic elements, such as ( 118), consist of unstable isotopes with lifetimes under milliseconds, synthesized in particle accelerators by fusing lighter nuclei. These components underpin elemental identity and behavior, with protons dictating periodicity and electron configurations explaining bonding trends across the periodic table.

Earth and biological contexts

The Earth's crust, comprising the outermost layer approximately 5–70 km thick, consists primarily of oxygen (46.6 wt%), silicon (27.7 wt%), aluminum (8.1 wt%), iron (5.0 wt%), calcium (3.6 wt%), sodium (2.8 wt%), potassium (2.6 wt%), and magnesium (2.1 wt%), with these elements forming the bulk of silicate minerals and oxides. The mantle, extending to about 2,900 km depth, is dominated by oxygen (44.33 wt%), magnesium (22.17 wt%), silicon (21.22 wt%), and iron (6.30 wt%), reflecting peridotite-like compositions rich in olivine and pyroxene. The core, divided into outer liquid and inner solid regions, is mainly an iron-nickel alloy, with iron comprising roughly 85–90% and nickel 5–10%, alongside lighter elements such as sulfur or oxygen potentially alloyed at 5–10% to account for density and seismic properties. In biological systems, a subset of elements cycles between Earth's reservoirs and organisms via biogeochemical processes, with carbon, hydrogen, oxygen, nitrogen, phosphorus, and sulfur (CHNOPS) forming over 99% of living biomass by mass. In the human body, oxygen constitutes about 65%, carbon 18.5%, hydrogen 9.5%, nitrogen 3.2%, phosphorus 1%, and sulfur 0.25%, primarily incorporated into water, proteins, nucleic acids, lipids, and carbohydrates. These macronutrients enable core functions: carbon provides structural backbones, hydrogen and oxygen facilitate energy transfer and hydration, nitrogen supports genetic and enzymatic roles, phosphorus enables energy storage (ATP) and membranes, and sulfur aids protein folding and redox reactions. Essential trace elements, required in parts per million or less, include iron (for oxygen transport in hemoglobin and electron transfer), zinc (cofactor in ~9% of eukaryotic proteins for catalysis and DNA binding), magnesium (chlorophyll and enzymatic activation), and others like copper, manganese, and molybdenum for redox and metabolic processes. Biogeochemical cycles—such as the carbon cycle (fixation via photosynthesis, release by respiration/decomposition) and nitrogen cycle (fixation by bacteria, assimilation into amino acids)—transfer these elements from lithospheric, atmospheric, and oceanic pools into biomass, with human activities altering fluxes (e.g., phosphorus mining for fertilizers disrupting sedimentary cycles). Biological selectivity favors bioavailable forms, concentrating rare crustal elements like phosphorus (0.13 wt% in crust but 1% in biomass) through evolutionary adaptations, while limiting toxic uptake of abundant ones like aluminum.

Mathematics

Elements in sets and structures

In set theory, an element, also termed a member, is a primitive object that belongs to a set, with the membership relation denoted by the symbol ∈, such that for a set A and object x, x \in A asserts that x is an element of A, while x \notin A denotes the negation. This relation forms the foundational predicate of , where sets are collections of distinct elements treated as entities, and elements themselves may be sets, enabling hierarchical constructions like the von Neumann ordinals. Axiomatic frameworks, such as Zermelo-Fraenkel , treat both sets and their elements as undefined primitives, with membership axioms like ensuring sets are determined by their elements: two sets are equal if they share exactly the same elements. Mathematical structures build upon sets by equipping a set of elements with operations and relations satisfying specific axioms. In a group, the elements form a non-empty set G paired with a \cdot: G \times G \to G that is associative, admits an e \in G such that e \cdot g = g = g \cdot e for all g \in G, and provides inverses g^{-1} \in G with g \cdot g^{-1} = g^{-1} \cdot g = e. Examples include the integers under , where elements are integers and the identity is 0. Rings extend this by requiring the elements to form an under addition, with a second distributive multiplication operation; for instance, the has elements \mathbb{Z}, addition as group operation, and multiplication satisfying distributivity. Fields represent a further refinement, comprising a with unity (multiplicative identity $1 \neq 0) where every non-zero element has a , enabling division except by zero. The rational numbers \mathbb{Q} exemplify a , with elements as fractions p/q ( p, q \in \mathbb{Z}, q \neq 0 ), addition and multiplication inherited from rationals, and inverses q/p for non-zero elements. Finite fields, such as \mathbb{F}_p for prime p, consist of elements \{0, 1, \dots, p-1\} under , underpinning applications in and . In these structures, elements serve as the carriers, with axioms constraining operations to preserve properties like closure, ensuring the structure's coherence and enabling theorems such as Lagrange's in groups or the fundamental theorem of fields.

Applications in algebra and geometry

In algebraic structures, elements function as the indivisible components upon which binary operations such as and are defined, facilitating the resolution of polynomial equations over fields like the real numbers. For instance, in , elements of polynomial rings enable factorization algorithms that underpin computer algebra systems for symbolic computation, as demonstrated in applications to Gröbner bases for solving systems of equations. These structures extend to modules over rings, where elements represent vectors in abstract vector spaces, allowing generalizations of geometric concepts like to non-Euclidean settings. Linear algebra exemplifies the interplay between algebraic elements and geometry, with vectors as elements of finite-dimensional vector spaces over a field modeling displacements and forces in . Matrices, composed of elements, encode linear transformations that preserve geometric properties such as parallelism and ratios of areas, essential for coordinate geometry and rendering. Eigenvalues and eigenvectors, derived from characteristic polynomials whose coefficients are matrix elements, quantify scaling factors along principal axes, applied in stability analysis of dynamical systems and for in data geometry. Geometric algebra further integrates these domains by constructing a where basis elements generate multivectors representing oriented geometric objects, such as lines as bivector elements and planes as trivectors. The geometric product of elements unifies inner and outer products, enabling conformal mappings for rotations and translations without matrices, with applications in ray tracing for realistic lighting in and kinematic chains in . This framework resolves ambiguities in vector cross products by treating intersections and projections as algebraic operations on elements, as utilized in for pose estimation from image correspondences.

Technology and Engineering

Electrical and circuit elements

Electrical circuit elements constitute the foundational components in the and of electrical circuits, modeling the relationships between voltage, , and under the lumped element , where circuit dimensions are small compared to signal wavelengths. These elements are classified primarily as passive or active: passive elements neither generate nor amplify electrical power but instead dissipate or store , while active elements can supply power to the circuit. The three canonical passive elements—, , and —form the basis for linear circuit theory, enabling the representation of real-world devices through idealized behaviors governed by differential equations. The opposes the flow of , converting into via , with its behavior defined by : V = I R, where V is voltage, I is current, and R is resistance in ohms. This principle was quantified by Georg Simon Ohm in 1827 through experiments demonstrating proportionality between current and voltage across conductors of uniform composition. Resistors are essential for , voltage division, and signal attenuation in circuits, with practical implementations ranging from carbon compositions developed in the to modern precision thin-film types. The stores electrical energy in an between two conductive plates separated by a , characterized by Q = C V, where Q is charge and C is in farads; its current-voltage relation is I = C \frac{dV}{dt}, allowing it to block while passing signals. The device originated with the , independently invented by Ewald Georg von Kleist in November 1745 and in 1746, which stored charge in water-filled glass jars and delivered shocks upon discharge, laying groundwork for electrostatic experiments. Modern capacitors, including electrolytic types patented by in 1866, are used for filtering, timing, and in power supplies. The , or , stores energy in a , opposing changes in per V = L \frac{dI}{dt}, where L is in henries; it passes but impedes high-frequency . Its principle stems from Michael Faraday's 1831 discovery of , where a changing induces voltage in a nearby , formalized as Faraday's . Inductors enable applications in filters, transformers, and oscillators, with early demonstrations using iron-core coils to produce continuous s. Active elements, such as independent voltage or current sources, provide fixed power regardless of circuit conditions, modeling batteries or generators that inject energy into the system. Dependent sources, like those in transistors invented in by Bardeen, Shockley, and Brattain, amplify signals by controlling output based on input variations, enabling and switching. These elements extend passive networks to realize complex functions, but their analysis requires consideration of non-linearities absent in ideal passives. In circuit simulation, tools like solve networks of these elements using Kirchhoff's laws and constitutive relations, validating designs against empirical measurements.

Computing and software elements

In , an element denotes a single constituent item within a , such as an or , where each element holds a value identifiable by an or . , for instance, consist of elements of uniform stored in contiguous locations, enabling efficient via indexing starting typically from zero. This usage facilitates operations like traversal, insertion, and deletion, with performance characteristics depending on the structure's implementation; for example, array averages O(1) in constant-time retrieval. In , particularly with markup languages like , an element comprises a start tag, optional attributes, , and an end tag, forming the foundational units that structure and render webpage . Examples include the <p> element for paragraphs or <img> for images, where elements can nest hierarchically to represent semantic relationships, influencing browser parsing and Cascading Style Sheets (CSS) application. As of standards finalized in 2014, over 100 defined elements exist, categorized by function such as (<head>), sectioning (<article>), or interactive forms (<input>), ensuring consistent interoperability across browsers. User interface (UI) elements in software applications refer to interactive or display components, such as buttons, text fields, and sliders, that enable user input and feedback within graphical environments. These elements, often termed widgets or controls, adhere to platform-specific guidelines—for instance, for specifies button elevations and effects for tactile response—prioritizing standards like WCAG 2.1, which mandate sufficient contrast ratios (at least 4.5:1 for normal text) to accommodate diverse users. In , UI elements integrate with event-handling systems, where user actions trigger callbacks, supporting modular design patterns like Model-View-Controller (MVC) to separate logic from presentation. Data elements, as defined in standards like those from NIST, represent of with unique semantics, such as a field for "date of birth" in a , underpinning data interchange formats like XML or . This concept extends to modeling, where elements delineate behavioral specifications, ensuring from user needs to implementation. Empirical studies, including those on code , highlight that precise element definitions reduce defect rates by up to 20% in large-scale systems through improved .

Materials and design elements

In materials engineering, design elements encompass the discrete structural units and modeling primitives used to fabricate and analyze components for technological applications, often leveraging the properties of constituent chemical elements to achieve desired performance characteristics such as strength-to-weight ratio and durability. Engineers classify materials into categories including metals (e.g., aluminum alloys with elements like magnesium for enhanced stiffness), polymers (incorporating carbon-based chains for flexibility), ceramics (utilizing and oxygen for high-temperature resistance), and composites (combining fibers like carbon with matrices for tailored ). These selections prioritize empirical metrics: for instance, steel's iron-carbon base yields tensile strengths exceeding 400 MPa in high-strength variants, enabling load-bearing in structures. A cornerstone of modern materials design is the (FEM), which discretizes complex material geometries into finite elements—simple shapes like triangles or tetrahedra—to solve partial differential equations governing , , and . Developed in the and refined through computational advances, FEM allows of material behavior under real-world conditions, such as predicting in (containing elements like for durability) subjected to cyclic loads up to 10^6 cycles. This approach reduces reliance on costly prototypes; for example, in , FEM models optimize composites to cut weight by 20-30% while maintaining crash resistance. Advanced applications integrate within FEM frameworks to bridge atomic-level interactions (e.g., in metallic crystals) with macroscopic outcomes, enabling the of metamaterials with negative Poisson's ratios for damping. Data-driven FEM variants, incorporating , further accelerate material discovery by predicting properties of novel alloys, as demonstrated in simulations achieving 95% accuracy for moduli in untested compositions. Such methods underscore causal links between composition, processing parameters (e.g., at 900-1200°C for phase transformations), and functional performance, informing designs in sectors like where silicon-based ceramics withstand photovoltaic thermal stresses exceeding 500°C.

Arts, Culture, and Entertainment

Literary and symbolic elements

Literary elements constitute the foundational components of narrative works, enabling authors to construct coherent and engaging stories. These include , which structures the sequence of events including exposition, rising action, climax, falling action, and resolution; characters, encompassing protagonists, antagonists, and supporting figures developed through traits, motivations, and arcs; setting, detailing the temporal and spatial context that influences events; and , the central ideas or messages explored, such as love, power, or mortality. Additional elements like , which determines narrative perspective (e.g., first-person or omniscient third-person), and , the driving tension between forces (internal or external), further shape reader interpretation and emotional impact. Symbolically, natural elements—earth, water, air, and fire—serve as archetypes in literature to evoke deeper meanings beyond their physical properties, rooted in ancient philosophical traditions and persisting in modern works. Earth typically represents stability, fertility, or groundedness, as in agrarian myths where it embodies nurturing yet unyielding permanence. Water symbolizes fluidity, emotions, or purification, often depicting change or subconscious depths, evident in flood narratives across cultures signifying renewal or destruction. Air conveys intellect, freedom, or ephemerality, linked to breath, wind, and inspiration in poetic motifs of aspiration or chaos. Fire, denoting transformation, passion, or peril, appears in alchemical and heroic tales to signify enlightenment or consuming force, such as in Prometheus myths where it ignites human progress amid risk. These symbols layer abstract themes onto concrete imagery, enhancing thematic resonance without explicit exposition, though interpretations vary by cultural context and author intent.

Music and performing arts

In music, the core elements comprise , which organizes sounds in time through patterns of and ; , a linear succession of pitches that forms recognizable tunes; and , the vertical arrangement of pitches into chords and progressions that support or contrast the . distinguishes sounds by their unique tonal quality, as produced by specific instruments or voices, while regulate intensity through variations in loudness, from (soft) to fortissimo (very loud). refers to the interplay of musical lines, categorized as monophonic (single line), homophonic ( with accompaniment), or polyphonic (multiple independent lines). Form provides the structural framework for compositions, such as (AB), (ABA), or , which organizes thematic development and repetition to convey progression. dictates the speed of the , measured in beats per minute, influencing emotional impact, while meter establishes recurring groups, like duple or , underpinning rhythmic stability. In , theater relies on Aristotle's six elements: , the sequence of events driving action; , the agents enacting the plot through motivations and traits; , the underlying ideas expressed; , the language and style of dialogue; , integrating vocal or instrumental elements; and , the visual aspects including and effects. Modern productions expand this to include technical components like , which shapes mood via color and intensity, and , amplifying dialogue, effects, and underscoring to enhance immersion. Dance performance centers on four primary elements: , the instrument of using limbs, torso, and gestures; , the dynamic force conveyed through sustained, percussive, or swinging qualities; , the pathways, levels, and shapes navigated onstage; and time, encompassing , , , and phrasing to synchronize motion. These elements interrelate with in interdisciplinary works, where choreographers align dance phrasing to rhythmic structures, as in ballet's adherence to pulses or contemporary pieces exploiting tension for expressive release. Across both and , elements function causally: and time propel momentum, while spatial and textural choices dictate perceptual focus, enabling audiences to discern coherence amid complexity.

Visual and media elements

In visual arts and design, the fundamental building blocks known as the elements of art include line, shape, form, space, color, value, and texture. Line is defined as a mark made by a moving point, varying in direction, width, and intensity to guide the viewer's eye or convey movement. Shape refers to two-dimensional areas enclosed by lines or defined by color contrasts, categorized as geometric (regular, like circles or squares) or organic (irregular, like natural forms). Form extends shape into three dimensions, creating the illusion of volume through shading or actual sculptural depth. Space encompasses positive areas occupied by objects and negative surrounding areas, manipulated via perspective or overlap to suggest depth. Color involves hue, saturation, and brightness, influencing mood and focal points through properties like complementary contrasts. Value denotes lightness or darkness of tones, essential for creating contrast and three-dimensional effects via chiaroscuro techniques. Texture describes surface quality, either tactile (actual feel) or visual (implied through patterns), adding realism or emphasis. These elements, as outlined in art education frameworks, form the vocabulary artists use to compose works across painting, sculpture, and digital media. In and , these elements integrate with principles like and to structure layouts, where line and shape define boundaries, color and establish emphasis, and prevents overcrowding for clarity. For instance, in poster design, high-contrast shifts draw attention to key text or imagery, while overlays simulate in digital renders. Empirical studies in design cognition confirm that mastery of these elements correlates with viewer comprehension and aesthetic preference, as measured by eye-tracking and preference surveys in controlled experiments. Within media production for , visual elements extend to —encompassing sets, props, , costumes, and actor positioning—which collectively construct space and character psychology before the camera. , as a core element, manipulates shadows and highlights to denote time, emotion, or realism, with techniques like standardizing illumination since the 1930s era. Cinematographic choices in shots (wide for context, close for intimacy) and angles (low for power dynamics) further these elements, while adjusts palettes for thematic consistency, as in desaturated tones for dystopian settings. Editing sequences integrate these by juxtaposing visual motifs, creating rhythm through cuts measured in milliseconds for tension, per analyses of classical montage theory. These components, verified through production breakdowns of films like (1941), demonstrate causal links between visual orchestration and audience immersion, supported by research on visual storytelling efficacy.

Business and Society

Corporate entities

Element Solutions Inc. is a specialty chemicals company headquartered in Fort Lauderdale, Florida, with operations focused on providing formulations for electronics, industrial coatings, and energy infrastructure applications. Originally established in 2013 as Platform Specialty Products Corporation, it rebranded to Element Solutions Inc. in 2019 while tracing operational roots to pioneering metal finishing chemistry developed as early as 1785. The firm reported $2.18 billion in net sales for fiscal year 2023, serving end-markets including printed circuit boards and consumer packaging. Element Materials Technology, a London-based provider of testing, , and services for materials and products, was formed in through a of Stork B.V.'s testing division. Specializing in destructive and non-destructive testing for sectors like , , and , the company operates over 200 facilities worldwide and employs approximately 7,000 people. Temasek Holdings acquired a majority stake in , valuing the business at around $7 billion. Its historical origins extend to 19th-century industrial testing practices in the UK. Element Fleet Management Corp., founded in 2007 and headquartered in , , offers leasing, financing, and management services for fleets, including , accident management, and integration. Listed on the (TSX: EFN), it manages over 1.2 million vehicles globally and reported $1.74 billion in revenue for 2023, emphasizing cost reduction through data-driven analytics. The company evolved from earlier fleet operations, including acquisitions like GE Capital Fleet Services in 2013. Other notable entities include , established in 2007 in as a manufacturer of affordable like televisions and soundbars, targeting budget-conscious markets with products assembled in . Element Resources LLC operates as a major U.S. lead-acid battery recycler, processing over 250,000 tons annually through smelting and polymer separation at facilities in and . These firms illustrate diverse applications of the "Element" branding in , , and services, often evoking reliability and foundational components.

Legal and military elements

In legal contexts, an "element" refers to a constituent part of a crime, tort, or other cause of action that must be proven to establish liability. For criminal offenses, these typically include actus reus (a voluntary criminal act or omission), mens rea (a culpable mental state, such as intent or recklessness), concurrence between the act and intent, causation, and sometimes attendant circumstances or a specified result. All elements must be established beyond a reasonable doubt by the prosecution in criminal trials; failure to prove any one defeats the case. For instance, in a charge of larceny, elements encompass the taking and carrying away of another's personal property, with intent to permanently deprive the owner. Civil claims similarly require proof of specific elements by a preponderance of the . In negligence suits, these comprise , of that duty, causation, and resulting . Statutory definitions delineate elements precisely to ensure , as affirmed in cases interpreting the Sixth Amendment. Legal scholars emphasize that elements serve as analytical tools for courts to dissect claims, preventing overreach by requiring factual specificity rather than generalized allegations. In and organization, an "element" denotes a functional subunit within a larger formation, often the smallest tactical building block in task-organized forces. It is typically formed around a specific , such as a security element, fire support element, or command element, enabling flexible mission adaptation. U.S. doctrine, for example, integrates elements into operational and , where they represent discrete capabilities like or detachments subordinated to a . This structure facilitates , with elements scalable from teams of a few personnel to specialized groups in operations. Force structure analyses highlight elements as core to assessing readiness, encompassing personnel, , and sustainment components across services. In , elements emphasize cohesion and maneuver; historical doctrines, such as those from task forces, underscore their role in decentralized execution under unified intent. Unlike rigid hierarchies, modern usage prioritizes elements to counter asymmetric threats, as seen in operations where intelligence elements integrate with maneuver units.

Modern Developments and Interdisciplinary Uses

Recent scientific advancements

In 2024, researchers at successfully synthesized (element 116) using a beam of titanium-50 ions accelerated at the 88-Inch Cyclotron, marking the first use of this isotope for production and offering a pathway to attempt element 120 by fusing titanium-50 with californium-249 targets. This method bypasses limitations of the traditional beams, which have been central to discoveries of elements 114–118, by providing higher reaction cross-sections for heavier targets. By , a collaborative effort at the produced two atoms of via a novel vanadium-51 beam on curium-243, demonstrating viability for pursuing elements beyond 118 and advancing toward the predicted "" where superheavy nuclei might exhibit enhanced longevity. In July 2025, new isotopes livermorium-288, livermorium-289, and copernicium-280 were identified through experiments at superheavy element factories, expanding knowledge of decay chains and nuclear shell structures in this regime. A June 2025 experiment yielded a new isotope of (element 106), providing insights into alpha-decay patterns and nuclear stability for transactinides, while August 2025 saw the development of an advanced atom-at-a-time chemistry technique at Berkeley Lab, enabling gas-phase reactions with superheavy elements like to probe relativistic effects on bonding. In March 2025, scientists characterized berkelocene, the first stable organometallic complex featuring (element 97), revealing unexpected five-coordinate geometry due to the actinide's 5f-electron influence. These developments underscore ongoing refinements in accelerator technology and detection, though no new elements have been officially verified since in 2016, with efforts focused on overcoming fusion barriers for Z > 118.

Emerging technological applications

In the transition to renewable energy systems, rare earth elements such as neodymium and dysprosium are increasingly vital for fabricating high-strength permanent magnets used in electric vehicle motors and offshore wind turbines, with demand expected to rise fourfold by 2040 in net-zero emission scenarios due to their superior magnetic properties enabling compact, efficient designs. Lithium, nickel, cobalt, and graphite underpin advanced battery chemistries, including nickel-manganese-cobalt cathodes in high-energy-density lithium-ion cells, while emerging solid-state batteries incorporating lithium metal anodes and sulfide electrolytes demonstrate prototypes with over 1,000 cycles and energy densities exceeding 400 Wh/kg as of 2024, addressing limitations in liquid electrolytes like flammability and dendrite formation. Advanced semiconductors rely on compound materials involving , , and for high-electron-mobility transistors in 5G base stations and , where devices operate at frequencies up to 100 GHz and handle voltages over 600 V, outperforming in efficiency for data centers and electric grids; the U.S. Department of Energy identified as short-term critical through 2025 due to its role in these applications. , a rare earth, enhances semiconductor doping to improve electrical and magnetic properties in compounds like for microwave filters. In and , rare earth ions such as and are doped into host crystals like yttrium orthosilicate for qubits exhibiting times exceeding 1 second at cryogenic temperatures, enabling scalable quantum networks via telecom-compatible wavelengths around 1,550 nm; recent 2025 analyses highlight their foundational role amid supply vulnerabilities, as controls over 90% of global rare earth processing. Two-dimensional , composed of transition metals like and carbon or , show promise in flexible supercapacitors with capacitances up to 1,500 F/g and electromagnetic interference shielding effectiveness over 90 dB, positioning them for wearable electronics and as recognized in IUPAC's 2024 list. , nanoscale zero-dimensional , facilitate optoelectronic applications in LEDs and sensors with quantum yields above 80%, leveraging their and tunability for biomedical imaging without heavy metals like .