On (Egyptian: Iunu, meaning "City of the Pillar"; Biblical Hebrew: ʾŌn) was an ancient city in Lower Egypt, approximately 10 miles northeast of modern Cairo in the Nile Delta, serving as the capital of the 13th nome and a paramount center of solar worship dedicated to deities including Atum, Ra, and Re-Horakhty.[1][2] The city originated influential Heliopolitan creation myths positing the primordial mound emerging from Nun waters, with Atum self-creating and generating the cosmos through his offspring Shu and Tefnut, embedding it deeply in Egyptiantheology and influencing later national priesthoods.[3] Its vast temple enclosure, measuring roughly 1,100 by 900 meters, housed monumental obelisks—such as the 21-meter granite one erected by Thutmose III around 1475 BCE, later relocated to New York City's Central Park—and functioned as a theological hub from the Old Kingdom onward, though systematic quarrying from medieval times onward reduced much of its structures to scattered ruins at Matariya.[4][5] In biblical accounts, On appears as the home of Potiphera, priest whose daughter Asenath married Joseph, highlighting its prominence during the late Middle Bronze Age.[2][6] Archaeological efforts, including Italian missions from 1903–1906 and recent excavations, have uncovered temple foundations and artifacts affirming its role in sustaining solar theology amid Egypt's dynastic shifts, despite limited preservation due to urban encroachment and reuse of materials.[1][5]
Language and linguistics
Preposition and adverb
In English, "on" functions primarily as a preposition denoting position or contact with a surface, as in "the book lies on the table," where it specifies a relation of support or attachment without enclosure.[7] It also serves as a preposition for temporal references to specific days or dates, such as "the meeting is on Monday" or "born on July 4, 1776," distinguishing it from broader periods.[8] As an adverb, "on" indicates continuation of an action or state, exemplified by "the performance must go on" or "the switch is on," often implying operational persistence.[9] These roles emerge empirically in syntactic analyses, where "on" governs noun phrases to express locative or stative semantics, as observed in corpora like the Pattern Dictionary of English Prepositions, which logs frequent collocations such as "dependent on" for reliance or "focus on" for directed attention.[10]Etymologically, the English "on" derives from Old English on, a preposition and adverb meaning "in" or "on," tracing to Proto-West Germanic ana and sharing Indo-European roots with terms like Old High Germanana for "on" or "upon."[11] This heritage reflects a core semantic of superposition or proximity, preserved in Middle English forms like an or on, and evident in historical texts such as the Anglo-Saxon Chronicle's use of on for positional descriptions (e.g., events "on þære tide" for "at that time").[11] Linguistic corpora confirm continuity, with modern usage aligning closely to these ancient patterns in over 90% of spatial preposition instances analyzed in the British National Corpus.[12]Spatially, "on" contrasts with "in" (enclosure or volume, e.g., "in the room") and "at" (precise point, e.g., "at the door") by evoking two-dimensional support, as in "standing on the platform," a distinction rooted in perceptual geometry where surfaces permit extension without containment.[13] Temporally, this logic extends: "on" applies to discrete units like days ("on Friday") versus "in" for expansive intervals ("in 2025") or "at" for instants ("at noon"), patterns quantified in preposition usage studies showing "on" dominating 75% of day-specific references in sampled English texts.[8] In related Germanic languages like German (auf for elevated "on") or Dutch (op), analogous forms maintain this surface-oriented semantics, underscoring a shared Proto-Germanic causal framework for relational encoding.[11]
Phonetic and prosodic uses
In Japanese prosody, the term on (音, meaning "sound") denotes the mora, the primary phonetic timing unit underlying rhythm and meter in traditional poetry and music. Each on corresponds to a roughly equal duration in speech production, forming the basis for syllabic counts in forms like haiku (5-7-5 on) and tanka (5-7-5-7-7 on), where geminate consonants, long vowels, and small kana like tsu or n each count as a distinct mora.[14] This moraic structure contrasts with syllable-based prosody in many Indo-European languages, as Japanese speakers perceive and produce rhythmic beats aligned to mora boundaries rather than stress feet.[15]Empirical acoustic studies confirm the near-isochronous timing of morae in Japanese, with durations averaging 100-150 milliseconds per on in neutral speech, supporting its role in prosodic phrasing and intonation patterns.[16] In poetic recitation, this timing enforces a steady pulse, influencing pitch accent placement and facilitating mnemonic recall, as deviations disrupt perceived naturalness. Non-native adaptations of Japanese poetic forms, such as English haiku, often approximate on counts with syllables, though this overlooks phonetic distinctions like the independent mora status of coda n.[17]Pronunciation of the English word "on" exhibits dialectal variation in vowel quality and nasal realization, analyzed through formant frequencies and duration measures. In Received Pronunciation, the vowel is typically /ɒ/, with F1 around 600-700 Hz and F2 1000-1200 Hz, lengthening slightly before nasals; General American variants shift to /ɑ/ or /ɔ/, with lower F1 values (500-600 Hz) reflecting monophthongization.[18] Acoustic comparisons across dialects, including rhotic influences in regions like Lancashire, reveal prosodic effects where "on" in phrase-final position undergoes nasalization and duration reduction, impacting intonation contours.[19] These variations arise from historical vowel shifts, verifiable via spectrographic data from corpora like the English Lexicon Project.
Science, technology, and mathematics
Mathematics
In mathematics, the preposition "on" denotes the underlying space or domain to which a mathematical structure or operation applies. A function defined on a set X to a codomain Y is a mapping f: X \to Y that assigns each element of X to exactly one element of Y, with this formulation central to set-theoretic foundations since the late 19th century.[20] Similarly, a binary relation on a set X is a subset of the Cartesian product X \times X, capturing pairwise associations within X, as formalized in early axiomatic set theory.[21]Group actions exemplify this usage: a group G acting on a set X consists of a map G \times X \to X satisfying identity and compatibility conditions, equivalent to a homomorphism G \to \mathrm{Sym}(X), the symmetric group on X. This framework, tracing to permutations studied by Cauchy around 1845, enables counting orbits via Burnside's lemma, where fixed points of group elements on X determine orbit sizes.[22][23]In topology, a topology on a set X is a family of subsets (open sets) closed under arbitrary unions and finite intersections, endowing X with continuity notions without a metric.[24] For manifolds in differential geometry, points lie on the manifold M, with local Euclidean structure; the tangent space at a point p on M comprises derivations or velocity vectors along curves through p, foundational for defining differentials and curvatures.[25] Riemannian metrics on M assign inner products to tangent spaces at each point, enabling distance measurements, as developed by Bernhard Riemann in 1854.[26]
Physics and chemistry
In particle physics and quantum field theory, "on-shell" refers to the condition where a particle's four-momentum p^\mu satisfies the relativistic dispersion relation p^2 = m^2 c^2 (in natural units, p^2 = m^2), meaning its energy E and three-momentum \mathbf{p} obey E^2 = \mathbf{p}^2 c^2 + m^2 c^4.[27] This constraint arises from the field's equations of motion, such as the Klein-Gordon equation for scalars or Dirac equation for fermions, ensuring the particle behaves as a free, propagating entity observable in detectors.[28] Causally, on-shell propagation corresponds to real particles exchanging energy and momentum consistently with conservation laws over macroscopic distances, as validated in collider experiments where decay products' invariant masses peak at the parent's rest mass; deviations indicate off-shell virtual particles confined to interaction vertices.[27]The distinction gained prominence in the 1940s with the formulation of quantum electrodynamics by Feynman, Schwinger, and Tomonaga, where off-shell propagators \frac{i}{p^2 - m^2 + i\epsilon} in perturbation theory allow virtual particles to mediate forces without direct observation, but renormalization enforces on-shell physical parameters like masses and charges measured in scattering cross-sections.[29] Experimental confirmation includes electron-positron annihilation to muons at CERN's LEP collider (1989–2000), where on-shell muon pairs reconstructed the Z boson's mass at 91.1876 ± 0.0021 GeV with high precision, excluding off-shell contributions below detection thresholds. In lattice quantum chromodynamics simulations since the 1980s, on-shell conditions extract hadron masses from correlation functions, matching empirical data from facilities like Jefferson Lab.[28]In physical chemistry and surface science, "on" describes adsorption and reaction processes occurring on solid substrates, as in the Eley-Rideal mechanism where a gas-phase molecule reacts directly with an adsorbed species on a catalyst surface, contrasting homogeneous gas-phase reactions./Kinetics/Reaction_Mechanisms/Catalytic_Mechanisms) This usage highlights causal pathways in heterogeneous catalysis, where binding energies dictate activation barriers; for instance, ammonia synthesis on iron catalysts since the Haber-Bosch process (1910) involves nitrogendissociation on surface Fe atoms, with rates scaling via Langmuir adsorption isotherms fitted to turnover frequencies measured at 400–500°C and 100–300 atm. Spectroscopic techniques like sum-frequency generation, developed in the 1980s, probe vibrational modes "on" interfaces, revealing orientational order that governs wetting and reactivity, as evidenced by alkyl chain alignment on silica surfaces altering hydrophobicity.
Biology and medicine
In cancer biology, oncogenes represent mutated forms of proto-oncogenes that promote uncontrolled cell proliferation by remaining constitutively active, akin to a persistent "on" switch in regulatory pathways. These genes, numbering around 100 identified to date, were first characterized through studies of retroviral transforming genes in the 1970s and 1980s, with key examples including RAS and MYC, which drive tumorigenesis when overexpressed or altered. Empirical evidence from transfection assays and transgenic mouse models demonstrates their causal role in malignant transformation, as inhibiting oncogene activity via targeted therapies like tyrosine kinase inhibitors reduces tumor growth in clinical trials.[30][31]In retinal physiology, ON bipolar cells constitute a class of second-order neurons that depolarize in response to light onset, facilitating the detection of increments in illumination within the visual field. These cells, distinguished from OFF bipolar cells by their use of metabotropic glutamate receptors that invert photoreceptor signals, were delineated through electrophysiological recordings in vertebrate retinas, showing sustained depolarization to central light spots in ON-center variants. Neuroimaging and patch-clamp studies confirm their role in parallel ON and OFF pathways projecting to ganglion cells, essential for contrast sensitivity and motion detection, with disruptions linked to visual disorders like congenital stationary night blindness.[32][33][34]In Parkinson's disease management, the "ON" state refers to periods of improved motor function following levodopa administration, contrasting with "OFF" episodes where bradykinesia, rigidity, and tremor reemerge due to waning dopamine levels. Affecting over two-thirds of patients with advanced disease, these fluctuations arise from progressive loss of nigrostriatal neurons and erratic pharmacokinetics of dopaminergic therapies, as quantified in longitudinal studies tracking daily symptom diaries and wearable sensors. Clinical trials of adjunct therapies, such as COMT inhibitors, have extended ON duration by 1-2 hours on average, underscoring the therapeutic focus on stabilizing these states through dopamine modulation verified by PET imaging of striatal uptake.[35][36]
Computing and technology
In digital computing, the term "on" denotes the active state in binarylogic, where a high voltage level (typically representing logic1) allows current to flow through transistors or switches, contrasting with the "off" state (logic0) that blocks flow.[37] This on/off duality underpins all electronic computation, enabling Boolean operations like AND, OR, and NOT via logic gates, with transistors operating in saturation (fully on) for minimal power dissipation.[38] The foundational application of such binary electronic switching emerged in the 1940s with relay-based and vacuum-tube circuits, evolving into transistorized systems by the 1950s that standardized on/off states for scalable data processing.[39]ON Semiconductor, a major producer of semiconductor components, exemplifies corporate use of "on" in branding, specializing in power management integrated circuits (ICs), sensors, and analog/digital logic chips that control on/off switching in devices like automotive electronics and industrial systems.[40] Founded on October 4, 1999, as a spin-off from Motorola's semiconductordivision, the company reported $8.25 billion in revenue for fiscal year 2023, with products enabling efficient on-state conduction in MOSFETs and IGBTs rated up to 1200V for high-power applications.[41]In modern networking protocols, "always-on" describes persistent connectivity states, particularly in 5G architectures standardized by 3GPP Release 15 in 2018, where devices maintain low-latency, uninterrupted links via enhanced control plane signaling and beamforming to support massive IoT deployments.[42] This capability, achieving sub-1ms latency and up to 10 Gbps throughput in trials by 2019, relies on power-efficient on-states in RF front-ends and baseband processors to minimize battery drain during idle-yet-connected modes.[43] Deployment milestones include Verizon's 5G always-on pilots in 2019, enabling real-time applications like remote surgery and autonomous vehicles without traditional session re-establishment.[44]
Places
Geographical locations
On, known in ancient Egyptian as Iunu (or Iwnw) and rendered as "On" in the Hebrew Bible, refers to the site of Heliopolis, a major predynastic and Old Kingdom city in the Nile Delta region of Lower Egypt. Located at approximately 30°07′46″N 31°18′26″E near modern Cairo, it served as a primary cult center for the sun god Ra and featured monumental structures including obelisks and temple complexes dating to the Third Dynasty (c. 2686–2613 BCE).[45] Archaeological excavations have uncovered Bronze Age artifacts, such as granite pillars and statues from the Fifth Dynasty (c. 2494–2345 BCE), confirming continuous occupation from at least 3000 BCE.[46] The site's etymology ties to its role as a "pillar city," symbolizing the benben stone representing the primordial mound of creation in Egyptian cosmology.[47]Limited modern locales bear the name "On," often as minor or historical designations without significant population or elevation data in official gazetteers. No verified settlements named "On" appear in U.S. censuses or Turkish topographic records near the Black Sea with Bronze Age ties.[48]
Administrative divisions
In ancient Egypt, On—known in Egyptian as Iunu and later Hellenized as Heliopolis—functioned as the capital of the Heliopolite Nome, one of the principal administrative divisions of Lower Egypt dating to the Early Dynastic Period around 3100 BCE.[49] This nome encompassed fertile lands along the Nile Delta, supporting agricultural taxation, temple estates, and local governance under nomarchs appointed by the pharaoh, who oversaw irrigation, labor conscription, and tribute collection.[50] The city's administrative prominence stemmed from its role as a theological hub for the sun god Ra, integrating religious authority with secular control over resources vital to the state's economy.[45]Biblical references identify On explicitly as a fortified city in Genesis 41:45 and 41:50, linking it to Joseph’s era and underscoring its enduring status as an administrative entity under pharaonic oversight, with records of priestly bureaucracies managing vast temple complexes that doubled as economic centers.[51] By the Old Kingdom (ca. 2686–2181 BCE), the nome's structure facilitated centralized pharaonic rule, evidenced by pyramid texts and administrative papyri detailing land surveys and fiscal accounts tied to Heliopolis.[52] No modern sovereign administrative divisions bear the name "On" with equivalent historical or demographic significance, though minor locales exist without formal divisional status.
Arts and entertainment
Music
"ON" is a song recorded by the South Korean boy band BTS, released on February 21, 2020, as the title track and opening song of their fourth studio albumMap of the Soul: 7.[53] The track features a hip-hop-influenced production with orchestral elements, marching drum beats, and themes of perseverance and unity, co-written by members RM, SUGA, and J-Hope alongside producers Pdogg and 20.[54] It debuted at number four on the Billboard Hot 100, marking BTS's highest-charting single at the time, and topped charts in South Korea and Japan.[55]A remix version featuring Australian singer Sia was released digitally on February 27, 2020, incorporating electronic and pop elements while retaining the original's motivational lyrics.[56] The song's music video, directed by Yong-seok Choi, depicts the group in a colossal abandoned structure symbolizing struggle and resilience, amassing over 1 billion views on YouTube by 2023.[53] Performances included live renditions on shows like The Tonight Show Starring Jimmy Fallon, where BTS took over Grand Central Terminal in New York on February 24, 2020.[57]
Film, television, and literature
"On" is a science fiction novel by British author Adam Roberts, published in 2001 by Gollancz as his second full-length work of fiction.[58] The narrative explores human societies contending for survival in a resource-scarce environment, structured around philosophical and existential themes without relying on traditional interstellar tropes. Roberts, known for blending speculative elements with literary prose, drew from influences in hard science fiction while emphasizing societal dynamics over technological exposition.[59] No major feature films or television series bear the exact title "On," though independent short films with this name have appeared in niche festivals, such as experimental works from the early 2010s focusing on abstract human interactions.[60] In theater, productions titled simply "On" are rare, with most references pointing to adaptations or one-act plays in regional circuits rather than established dramatic works.
Other creative works
No notable visual arts installations, paintings, or sculptures titled simply "On" have achieved widespread recognition in major collections or exhibitions post-2000. Similarly, theater productions, dance choreographies, or indie video games bearing the exact title "On" lack prominent documentation in professional repertoires or gaming databases, distinguishing these categories from more descriptive or compound titles in creative works. Performance art pieces under this moniker are also undocumented in key historical surveys of the medium.
Other uses
Historical and mythological
The city of On, known in ancient Egyptian as Iunu (or Iunu shemau for the northern district), corresponds to the site of Heliopolis, a prominent religious and cultural center in Lower Egypt near modern Cairo. Established during the Predynastic Period around 3100 BCE, it served as the capital of the 13th nome and became a focal point for solar theology by the Early Dynastic Period (c. 3100–2686 BCE), with archaeological evidence including temple foundations and obelisks dating to the Old Kingdom (c. 2686–2181 BCE).[1]In biblical tradition, On appears in Genesis 41:45, identifying it as the residence of Potiphera, a priest whose daughter Asenath married the Hebrew figure Joseph during his rise in Egyptian administration, traditionally dated to the Middle Bronze Age (c. 2000–1550 BCE). This reference aligns with Heliopolis's role as a priestly hub, though the historicity of the Joseph narrative remains debated among scholars due to limited direct corroboration in Egyptian records beyond the city's prominence in administrative and religious contexts.[47][61]Mythologically, On/Heliopolis anchored the Heliopolitan cosmogony, one of ancient Egypt's primary creation accounts, wherein the god Atum self-generated from the chaotic waters of Nun atop the primeval mound (benben) at the city's temple, subsequently creating Shu (air) and Tefnut (moisture) through masturbation or spitting, leading to the Ogdoad and Ennead of deities. This narrative, preserved in Pyramid Texts from the 5th Dynasty (c. 2494–2345 BCE), emphasized solar rebirth and influenced later Egyptian theology, distinguishing it from rival cosmologies at Hermopolis or Memphis by prioritizing Atum's solitary emergence over primordial pairs.[62]
Business and organizations
On Holding AG is a Swissmultinational corporation specializing in athletic footwear, apparel, and accessories, particularly known for its CloudTec cushioning technology in running shoes. Founded on January 1, 2010, by former Ironman triathlete Olivier Bernhard, along with David Allemann and Caspar Coppetti, the company is headquartered in Zurich and focuses on performance-oriented products designed to enhance movement and reduce impact.[63] It went public on the New York Stock Exchange in September 2021 under the ticker ONON, with operations expanding to over 60 countries and annual revenues exceeding $1.5 billion as of 2023.[64]onsemi (formerly ON Semiconductor Corporation) is an American semiconductor manufacturer producing components such as power management, sensors, and analog integrated circuits for automotive, industrial, and communications applications. Established as a spin-off from Motorola's Semiconductor Components Group on July 4, 1999, it was headquartered initially in Phoenix, Arizona, before relocating to Scottsdale.[40] The company rebranded to onsemi in 2021 and reported net sales of approximately $8.3 billion in 2022, employing around 26,000 people globally.[41]
Miscellaneous
"ON" is the conventional abbreviation in linguistics for Old Norse, a North Germanic language spoken by Vikings and medieval Scandinavians from roughly the 8th to the 14th centuries, preserved in texts such as the Icelandic sagas and eddas.[65] This usage distinguishes it from modern Scandinavian languages and highlights its role in etymological studies of English words borrowed via Norse influence, like "sky" or "window."[65]In computing and networking, "ON" refers to Open Network, an architecture promoting vendor-neutral hardware and software interoperability to reduce proprietary lock-in, as advanced by initiatives like the Open Networking Foundation established in 2011. Such systems enable programmable data planes, facilitating innovations in software-defined networking observed in deployments by major cloud providers since the mid-2010s.Medically, "ON" abbreviates optic neuritis, an inflammation of the optic nerve often linked to demyelinating diseases like multiple sclerosis, with incidence rates around 1-5 per 100,000 annually in Western populations and typical symptoms including acute vision loss and pain on eye movement. Diagnosis relies on MRI evidence of lesions and visual evoked potentials, with treatments like corticosteroids reducing recovery time in acute cases.