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Normal

Normal is a town in McLean County, central Illinois, United States, and the only incorporated municipality in the nation named "Normal."^[1] It serves as the northern component of the Bloomington-Normal metropolitan area, strategically positioned amid fertile corn and soybean fields at the intersection of major interstate highways, fostering a diverse economy centered on education, insurance, and manufacturing.^[2] With a population of approximately 52,000, the town is defined by its hosting of Illinois State University, originally established in 1857 as Illinois State Normal University—a teachers' college modeled on French écoles normales designed to train educators in standard pedagogical methods and societal norms—which directly inspired the community's name upon its formal incorporation in 1867.^[3]^[4]^[1] The town's development reflects pragmatic 19th-century priorities, evolving from a rail-linked settlement to a hub for higher education and industry, including a Mitsubishi Motors assembly plant producing vehicles for North American markets, while maintaining a high quality of life through connectivity and community planning.^[5]^[2] Its location along historic Route 66 further underscores its role in regional transportation and tourism, though it has avoided major controversies, prioritizing steady growth over rapid urbanization.^[6]

Science and Mathematics

Geometry and Physics

In geometry, a normal is a line or vector perpendicular to a given curve or surface at a specified point. For a plane curve, the normal line passes through the point of tangency and is orthogonal to the tangent line there, determined by the curve's derivative or parametrization.^[7] The principal unit normal vector \mathbf{N}(t) to a space curve parametrized by arc length is defined as \mathbf{N}(t) = \frac{\mathbf{T}'(t)}{\|\mathbf{T}'(t)\|}, where \mathbf{T}(t) is the unit tangent vector, pointing toward the direction of curvature.^[8] For planes, a normal vector is any nonzero vector orthogonal to all direction vectors lying within the plane, often used to define the plane's equation as \mathbf{n} \cdot (\mathbf{r} - \mathbf{r_0}) = 0, where \mathbf{n} is the normal and \mathbf{r_0} a point on the plane.^[9] On parametrized surfaces, the normal vector is the cross product of the partial derivatives of the parametrization, \mathbf{N} = \frac{\partial \mathbf{\Phi}}{\partial u} \times \frac{\partial \mathbf{\Phi}}{\partial v}, normalized to unit length for applications like shading in computer graphics or differential geometry.^[10] In physics, the normal force \mathbf{N} is the contact force component exerted by a surface on an object, directed perpendicular to the interface, balancing compressive interactions to prevent interpenetration; its magnitude equals the object's weight on a horizontal, non-accelerating surface under gravity, N = mg.^[11] ^[12] In optics, the normal refers to the line perpendicular to a reflecting or refracting surface at the point of incidence, serving as the reference for measuring angles: reflection obeys \theta_i = \theta_r, where \theta_i and \theta_r are incidence and reflection angles relative to the normal; refraction follows Snell's law, n_1 \sin \theta_i = n_2 \sin \theta_r, with light bending toward the normal when entering a denser medium (n_2 > n_1).^[13] ^[14]

Statistics and Probability

The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution characterized by its symmetric bell-shaped curve, where the mean, median, and mode coincide at the center.^[15] It is defined by two parameters: the mean \mu, which determines the location of the peak, and the standard deviation \sigma, which measures the spread, with the probability density function given by f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}}.^[15] This distribution models many natural phenomena due to its mathematical properties, including additivity under summation of independent random variables.^[16] Key properties include symmetry around the mean, such that the probability of a value falling above or below \mu is equal, and the total area under the curve equals 1, representing the full probability space.^[15] Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three, a rule derived from the integral of the density function over those intervals.^[17] The standardized normal distribution, with \mu = 0 and \sigma = 1, facilitates z-score transformations, z = \frac{x - \mu}{\sigma}, enabling table-based probability calculations for any normal variant.^[15] In probability theory, the central limit theorem (CLT) underpins the ubiquity of the normal distribution: for independent and identically distributed random variables with finite mean and variance, the distribution of the sample mean approaches normality as sample size n increases, regardless of the underlying population distribution, with convergence rate improving for n \geq 30.^[18] This justifies approximating binomial or Poisson outcomes as normal for large n, such as in np \geq 5 and n(1-p) \geq 5 for binomials.^[19] The CLT's implications extend to confidence intervals and hypothesis testing, where sample statistics are treated as normally distributed for large datasets.^[18] To assess normality empirically, statistical tests compare observed data against the normal model's expectations. The Shapiro-Wilk test, effective for small samples (n < 50), computes a W statistic measuring deviation from normality, rejecting the null hypothesis if p < 0.05.^[20] The Kolmogorov-Smirnov test evaluates the maximum difference between empirical and theoretical cumulative distribution functions, suitable for larger samples but less powerful against specific alternatives like skewness.^[20] Visual methods, including Q-Q plots comparing sample quantiles to normal quantiles, complement these, as tests alone can lack power for n < 100 or be sensitive to outliers.^[20] Non-normal data may require transformations like log or Box-Cox to approximate normality for parametric analyses.^[15]

Chemistry

In analytical chemistry, normality (N) denotes the concentration of a solution expressed as the number of gram equivalents of solute per liter of solution, where an equivalent is defined by the stoichiometric reacting capacity, such as the number of protons in acids or electrons in redox reactions.^[21] A normal solution is one with a normality of 1 N, containing one gram equivalent per liter, facilitating stoichiometric calculations in titrations without adjusting for valence or reaction specifics.^[21] For instance, sulfuric acid (H₂SO₄) in complete dissociation yields two equivalents per mole, so a 0.5 M solution is 1 N.^[22] Though less common today due to the preference for molarity (M), which is independent of reaction type, normality remains useful in contexts like acid-base and precipitation analyses where equivalent weights standardize comparisons.^[21] In physical chemistry, the normal boiling point of a liquid is the temperature at which its vapor pressure equals one standard atmosphere (760 mmHg or 101.325 kPa), marking the transition to boiling under typical laboratory conditions without specifying elevation or reduced pressure effects.^[23] For water, this is precisely 100 °C, serving as a reference for thermometers and purity checks in distillation.^[24] Similarly, the normal melting point is the temperature at which a solid melts at 1 atm, though boiling points are more frequently tabulated due to their sensitivity to intermolecular forces and utility in volatility assessments.^[25] These "normal" conditions contrast with IUPAC's standard state of 1 bar (100 kPa) adopted in 1982, but the 1 atm definition persists in many textbooks for historical compatibility.^[23] In organic nomenclature, "normal" designates unbranched, straight-chain hydrocarbons, prefixed as "n-" to distinguish from isomers; for example, n-pentane (CH₃(CH₂)₃CH₃) contrasts with isopentane, emphasizing linear carbon skeletons in systematic IUPAC naming for alkanes and derivatives.^[26] This convention, rooted in early 20th-century usage, aids in identifying primary structural motifs affecting properties like boiling points, where n-alkanes exhibit higher values than branched counterparts due to reduced surface area and stronger van der Waals interactions.^[26] The term extends to alkyl groups, such as n-propyl (CH₃CH₂CH₂-), underscoring acyclic linearity in substituent descriptions.^[26]

Other Scientific and Mathematical Concepts

In abstract algebra, a subgroup N of a group G is termed normal if for every g \in G, the left coset gNg^{-1} equals the right coset Ng^{-1}g, or equivalently, gNg^{-1} \subseteq N.^[27] This property ensures that the quotient group G/N forms a well-defined group structure under the operation = [ab], where $$ denotes the coset aN.^[28] Normal subgroups generalize the role of kernels in homomorphisms and are fundamental to the first isomorphism theorem, linking group structures via surjective maps. Trivial examples include the identity subgroup \{e\}, which is always normal, and the full group G itself.^[27] In linear algebra, a square matrix A over the complex numbers is normal if it commutes with its conjugate transpose, satisfying A^*A = AA^*, where A^* denotes the adjoint.^[29] This condition encompasses Hermitian matrices (A = A^*) and unitary matrices (A^* = A^{-1}) as special cases, but extends to broader classes where eigenvalues can be diagonalized by unitary transformations.^[30] Normal matrices preserve the Euclidean norm under conjugation, i.e., \|A\mathbf{v}\| = \|A^*\mathbf{v}\| for vectors \mathbf{v}, facilitating spectral analysis in quantum mechanics and signal processing.^[29] In topology, a normal space is a T_1 space (Hausdorff with singletons closed) where any two disjoint closed sets can be separated by disjoint open neighborhoods.^[31] This separation axiom exceeds regularity and enables the Tietze extension theorem, allowing continuous extension of real-valued functions from closed subsets to the whole space.^[32] Compact Hausdorff spaces are normal, as are metrizable spaces, but normality does not preserve under arbitrary subspaces; closed subspaces of normal spaces remain normal, though the product of normal spaces may fail normality in pathological cases like the Sorgenfrey plane.^[33] In physics, particularly vibrations and waves, a normal mode refers to a pattern of motion in a coupled oscillatory system where all components vibrate at a single frequency, expressible as a linear combination of independent eigenvectors of the system's dynamical matrix.^[34] These modes diagonalize the equations of motion, decoupling interactions; for instance, in a chain of masses connected by springs, normal modes correspond to standing waves with frequencies determined by eigenvalues, enabling analysis of energy distribution and resonance.^[35] The set of normal modes forms a complete basis for the configuration space, applicable to molecular vibrations, acoustics, and quantum field theory.^[34]

Definitions and Historical Etymology

In social and cultural contexts, "normal" denotes behaviors, conditions, or traits that align with prevailing social norms—shared, often unwritten expectations governing conduct within a specific group, community, or society.^[36] These norms function descriptively by reflecting statistical commonality or typicality, such as widespread practices like greeting acquaintances with a handshake in Western cultures, and prescriptively by prescribing ideal or required actions to maintain social order.^[37] Sociologists distinguish normality from mere frequency by emphasizing its role in defining boundaries of acceptability, where deviations may incur social sanctions, labeling individuals as deviant or marginal.^[38] The word "normal" originates from Late Latin normalis, formed from norma, referring to a carpenter's square or rule used for measuring right angles, implying something conformed to a precise standard.^[39] It entered English around 1520, initially in technical senses related to geometry and architecture, meaning perpendicular or at right angles to a line or plane, as in a "normal line" intersecting a curve orthogonally.^[40] By the late 17th century, its usage expanded to denote conformity to a type, rule, or average, shifting from literal measurement to abstract regularity. The term's application to human qualities and social behavior emerged in the early 19th century, influenced by statistical innovations like Adolphe Quetelet's "average man" (l'homme moyen), which equated social normality with the central tendency of population data.^[41] Prior to this period, "normal" was rarely predicated of people, remaining confined to mathematical or physical contexts; its social extension coincided with industrialization, colonial anthropometry, and emerging disciplines like sociology and psychology, where normality served to classify populations, health, and morality against quantifiable averages.^[42] This evolution tied normality to both empirical observation—e.g., body measurements or behavioral frequencies—and normative judgments, enabling categorizations of "abnormal" traits in fields like criminology and eugenics by the late 1800s.^[43]

Normality in Psychology and Biology

In psychology, normality is frequently assessed through statistical criteria, where behaviors, cognitions, or traits falling within the central portion of a population distribution—typically encompassing about 95% of cases under a normal (Gaussian) curve—are deemed normal, while extremes are considered abnormal. ^[44] This approach, rooted in quantitative deviation from the mean, underpins diagnostic thresholds in tools like intelligence testing, where scores between 85 and 115 IQ points represent normality for the general population.^[44] However, statistical normality does not equate to psychological health or functionality; for instance, widespread prevalence of suboptimal traits, such as average levels of anxiety in modern surveys exceeding historical baselines, can fall within "normal" ranges yet impair adaptive functioning. Functional perspectives complement statistical ones by defining normality as the capacity for effective adaptation to environmental demands without significant distress or impairment, aligning with evolutionary criteria of species-typical competence in survival and reproduction.^[45] ^[46] In clinical contexts, this manifests in criteria from diagnostic manuals emphasizing deviation from adaptive norms, such as persistent inability to maintain social or occupational roles, though such standards have evolved; pre-1952 editions of the American Psychiatric Association's diagnostic guide classified homosexuality as abnormal based on cultural norms, later revised amid empirical reevaluation of functionality.^[45] Analytical psychology extends this to a balanced psychic ecology, where normality involves sustainable integration of conscious and unconscious elements without overwhelming disequilibrium.^[47] Critiques highlight that equating normality with mere statistical prevalence risks pathologizing adaptive outliers, as seen in historical over-diagnosis of gifted individuals as disordered. In biology, normality refers to physiological or developmental states aligning with species-typical patterns observed in healthy populations, often quantified as reference ranges capturing 95% of variation in traits like blood constituents or organ function from reference cohorts.^[48] ^[49] These ranges derive from empirical distributions in non-diseased individuals, serving as benchmarks for homeostasis—such as core body temperature averaging 37°C with deviations signaling pathology—but do not guarantee individual optimality, as population averages may include subclinical inefficiencies.^[49] Biological normalcy further ties to normative judgments of adaptive fitness, distinguishing statistical centrality from idealized function; for example, deviations in embryonic development, like atypical limb formation in vertebrates, disrupt species-typical morphology essential for locomotion and survival.^[50] ^[51] Developmental biology emphasizes normality as adherence to conserved ontogenetic sequences across species, where "normal" trajectories involve timed cellular processes like proliferation and differentiation yielding functional adult forms, as evidenced in model organisms like Drosophila melanogaster, whose 13-segment larval pattern reliably precedes viable metamorphosis in wild-type strains.^[52] ^[53] Disruptions, such as mutations altering Hox gene expression, produce abnormal phenotypes diverging from species-typical bauplans, underscoring causality in normality as fidelity to evolved developmental programs rather than mere statistical frequency.^[53] In mammals, including humans, normal growth milestones—such as ambulation by 12-15 months in 95% of infants—reflect species-typical neurobiological maturation, with delays often linked to environmental or genetic factors impeding typical synaptic pruning and myelination rates documented in longitudinal cohort studies.^[54] This framework prioritizes causal mechanisms over descriptive averages, revealing that while variance exists, normality converges on reproducible, adaptive outcomes across generations.^[55]

Contemporary Debates and Controversies

One prominent contemporary debate centers on the neurodiversity paradigm versus the traditional medical model in understanding conditions like autism spectrum disorder (ASD). Proponents of neurodiversity, which gained traction in the late 1990s and expanded through online advocacy in the 2010s, argue that neurological differences such as autism represent natural human variations rather than deficits or pathologies requiring cure or normalization.^[56] This view posits that societal barriers, not inherent traits, primarily cause disability, advocating for accommodations over interventions like behavioral therapies aimed at conforming to neurotypical norms.^[57] Critics, including clinicians emphasizing empirical outcomes, contend that this framing understates verifiable impairments in social communication, sensory processing, and adaptive functioning documented in longitudinal studies, where untreated severe ASD correlates with higher rates of unemployment (up to 85% in adulthood) and co-occurring mental health issues.^[58] The medical model prioritizes evidence-based treatments, such as applied behavior analysis, which meta-analyses show reduce maladaptive behaviors by 47% on average, though neurodiversity advocates often label such approaches as coercive suppression of diversity.^[59] In gender and sexuality, debates intensify over whether gender dysphoria in youth constitutes a normal developmental variation or a condition warranting caution against hasty medicalization. The 2024 Cass Review, an independent systematic analysis commissioned by England's National Health Service, evaluated over 100 studies and found "remarkably weak" evidence supporting puberty blockers and cross-sex hormones for adolescents, with low-quality research plagued by small samples, lack of controls, and short-term follow-ups failing to demonstrate sustained benefits in mental health or gender congruence.^[60] It highlighted high desistance rates (up to 80-90% by adulthood) in pre-pubertal children with dysphoria when not medically transitioned, suggesting social influences and co-morbidities like autism (prevalent in 20-30% of cases) play causal roles overlooked by affirmation-only models.^[61]^[62] This led to UK restrictions on blockers outside trials and a shift toward holistic psychological assessments, contrasting with guidelines from bodies like the World Professional Association for Transgender Health, criticized for relying on activist-influenced evidence hierarchies that prioritize ideological affirmation over randomized trials, which remain ethically challenging but essential for causal clarity.^[63] Obesity's status as a pathological deviation from normal metabolic function or an acceptable bodily variation fuels another controversy, particularly amid rising prevalence (39% adult rate in the US as of 2020). The American Medical Association's 2013 classification of obesity as a chronic disease underscores its causal links to comorbidities, with meta-analyses showing BMI over 30 kg/m² elevating type 2 diabetes risk by 7-fold and cardiovascular mortality by 2-3 times, driven by adipose tissue inflammation and insulin resistance rather than mere size.^[64]^[65] While a subset exhibits "metabolically healthy obesity" (10-30% of cases, per cohort studies), long-term data reveal progression to metabolic dysfunction in over 50% within a decade, challenging body positivity narratives that frame obesity as neutral variation without addressing evolutionary mismatches in modern calorie-dense environments.^[66]^[67] These debates reflect broader tensions in psychology over "normalcy," where statistical prevalence (e.g., via big data) risks conflating commonality with health, as critiqued in analyses warning against pathologizing deviations while ignoring empirical harms from normalization of dysfunction.^[68]

Arts and Entertainment

Film and Television

"Normal" is the title of a 2003 American television drama film directed by Jane Anderson and produced by HBO Films, adapted from her play Looking for Normal. The story centers on Roy Applewood (Tom Wilkinson), a long-married factory worker in rural Illinois who reveals to his wife Irma (Jessica Lange) that he has felt female since childhood and intends to transition, straining family relationships while exploring themes of identity and acceptance. Featuring supporting performances by Clancy Brown and Hayden Panettiere, the film premiered at the Sundance Film Festival on January 20, 2003, and aired on HBO on September 14, 2003, receiving a 100% approval rating from critics on Rotten Tomatoes based on eight reviews.^[69]^[70] In 2025, "Normal" refers to a crime thriller film directed by Ben Wheatley, written by Derek Kolstad, and starring Bob Odenkirk as an interim sheriff in a small Minnesota town who investigates dark secrets following a bank robbery. Produced with elements of action and dark comedy, the film premiered at the Toronto International Film Festival on September 8, 2025, earning an 83% critics' score on Rotten Tomatoes from 23 reviews, with praise for Odenkirk's performance amid violent sequences involving yakuza elements. Magnolia Pictures acquired U.S. distribution rights and scheduled a wide release on April 17, 2026, in approximately 2,000 theaters.^[71]^[72]^[73] Other television productions titled "Normal" include a 2020 Israeli miniseries on Hot 3, following 24-year-old columnist Noam Ashkenazy's experiences in a psychiatric ward as he seeks personal stability, comprising eight episodes with an 8.1/10 IMDb rating from 62 users. A 2021–2022 British miniseries depicts expatriates attempting everyday life in America disrupted by chaotic events, rated 8.8/10 on IMDb from 134 ratings. Additionally, "Finding Normal" (2023), a faith-based film starring Candace Cameron Bure as a surgeon encountering community values in a rural Southern town, aired as a full-length feature emphasizing themes of rediscovery beyond urban norms.^[74]^[75]^[76] The concept of normality appears recurrently in film and television narratives critiquing suburban conformity, as in American Beauty (1999), where Lester Burnham (Kevin Spacey) rejects middle-class routines for personal fulfillment, or The Truman Show (1998), portraying Truman Burbank's (Jim Carrey) escape from an engineered "normal" existence in Seahaven. Such depictions often contrast idealized normalcy with underlying dissatisfaction, drawing from sociological observations of post-World War II American life.

Music

In music theory, particularly within the analysis of atonal and post-tonal music, the term "normal order" (also referred to as normal form) denotes the standardized, most compact ascending arrangement of the pitch classes in a set, minimizing the interval span between the lowest and highest pitches.^[77]^[78] This representation facilitates comparison across different transpositions or inversions of the same pitch-class set by prioritizing the configuration with the smallest overall diameter, typically determined by rotating the set until the largest gap between consecutive pitches aligns with the wrap-around from the highest to the lowest pitch class.^[79]^[80] To derive the normal order of a pitch-class set, analysts follow a systematic process: first, list the pitch classes in ascending order within one octave (using integers 0-11 modulo 12); second, generate all possible rotations of this sequence; third, select the rotation with the smallest interval between its first and last elements (the "span"); and fourth, in cases of ties, choose the rotation starting with the lowest-numbered pitch class.^[81]^[82] For example, the pitch-class set {0,1,4} (corresponding to a minor third plus semitone) has normal order [0,1,4], as its span of 4 semitones is smaller than alternatives like [1,4,0] (span 11) or [4,0,1] (span 9).^[83] This method ensures a unique canonical form for equivalence classes under transposition, aiding in the identification of set types without regard to octave or register.^[77] Normal order underpins broader tools in set theory, such as prime form (the normal order of a set or its inversion, whichever has the smaller first interval) and interval vectors, which quantify the distribution of intervals within the set for structural analysis.^[78]^[80] Originating in mid-20th-century analytical practices influenced by composers like Arnold Schoenberg and Milton Babbitt, it remains a foundational concept in post-tonal pedagogy, though critics note its limitations in capturing registral or timbral nuances in actual compositions.^[79] Applications extend to software tools for algorithmic composition and empirical studies of atonal textures, where normal order helps detect recurring motivic cells across works.^[82]

Literature and Other Media

"Normal" (2016), a speculative fiction novel by Warren Ellis, is set in a recovery facility for strategic foresight professionals suffering from "abyss gaze," a psychological affliction induced by prolonged contemplation of dystopian future scenarios; the protagonist uncovers anomalies suggesting broader conspiracies.^[84] Amy Bloom's 2002 historical novel "Normal" follows a World War I veteran searching for his missing wife, intersecting with early 20th-century explorations of sexual identity and personal reinvention in American society.^[85] Graeme Cameron's 2015 thriller "Normal," narrated in first person by an unnamed serial killer residing in rural England, examines the perpetrator's self-perception of ordinariness amid his crimes, blending horror with romantic elements.^[86] Sally Rooney's "Normal People" (2018) chronicles the intermittent relationship between two Irish university students from differing socioeconomic backgrounds, probing themes of intimacy, class disparity, and social conformity over several years; the novel sold over 500,000 copies in the UK alone by 2020 and received critical acclaim for its minimalist prose.^[87] Children's literature includes "Normal Norman" (2016) by Tara Lazar, a picture book challenging simplistic definitions of normality through a scientist's encounter with an unconventional bird, emphasizing individuality.^[88] "Normal: One Kid's Extraordinary Journey" (2010, graphic novel format updated 2019) by Magdalena and Nathaniel Newman recounts the latter's experiences with Treacher Collins syndrome, highlighting resilience against societal expectations of physical normalcy.^[89] In other media, "Normal People" was adapted into a 12-episode BBC/Hulu television series in 2020, directed by Lenny Abrahamson and Hettie Macdonald, starring Paul Mescal and Daisy Edgar-Jones; it garnered 16.5 million UK viewers for its premiere episode and won multiple awards, including two Emmys, for faithfully rendering the novel's interpersonal dynamics.^[90] The 2003 HBO television film "Normal," directed by Jane Anderson and starring Tom Wilkinson and Jessica Lange, portrays a long-married factory worker's decision to pursue sex reassignment surgery after decades of cross-dressing, confronting family upheaval and midlife identity shifts; it received a 71% approval rating on Rotten Tomatoes based on 14 reviews.^[69] "Next to Normal" (2008), a rock musical with book and lyrics by Brian Yorkey and music by Tom Kitt, centers on a suburban mother's bipolar disorder and its ripple effects on her family, questioning boundaries of emotional normality; it premiered on Broadway in 2009, earning three Tony Awards including Best Original Score.

Geography and Places

United States

Normal, Illinois, is a town in McLean County, central Illinois, with a population of 52,736 as of the 2020 United States Census. It forms the Bloomington–Normal metropolitan area alongside neighboring Bloomington, often referred to as the "Twin Cities," and serves as a hub for education, with Illinois State University—originally founded in 1857 as Illinois State Normal University—driving much of its economy and cultural life.^[1] The town was platted on June 7, 1854, initially as North Bloomington to distinguish it from the adjacent settlement, and incorporated on March 4, 1867, adopting the name "Normal" to reflect the nearby teacher-training institution, a term derived from French école normale schools focused on standard pedagogical methods.^[4] Historically tied to railroad development at the intersection of the Illinois Central and Chicago and Alton lines in the 1850s, Normal grew as a planned community promoted by figures like Jesse Fell, who developed early additions north and east of the original plat.^[4] The presence of the normal school, established by state legislation in 1857 amid competition from Bloomington and Peoria, solidified its identity as an educational center; the university remains the town's largest employer today, enrolling over 20,000 students as of 2023. Normal also lies along historic U.S. Route 66, featuring landmarks like preserved motels and signs that attract tourism, contributing to its economy alongside manufacturing and healthcare sectors.^[6] Beyond Illinois, smaller unincorporated communities bear the name Normal, such as Normal in Madison County, Alabama, established around 1890 near what became Alabama Agricultural and Mechanical University (formerly State Normal and Industrial School of Huntsville), though these lack independent municipal status. Minor locales in states like Tennessee, Indiana, and Kentucky exist but are rural or historical designations without significant population or infrastructure.^[91] Normal, Illinois, stands as the sole incorporated municipality with this name in the United States, emphasizing its unique etymological tie to educational norms rather than broader connotative uses of "normal."^[1]

Other Locations

A locality named Normal is situated in the municipality of Mercaderes, Cauca Department, southwestern Colombia, at an elevation of 1,143 meters above sea level.^[92] This minor settlement lies adjacent to the town of Mercaderes and lacks documented population figures or historical significance in available records, distinguishing it from more prominent U.S. locales sharing the name.^[91] No other verified geographical locations named Normal exist outside the Americas based on global place-name databases.^[91]

Transportation

Automobiles and Vehicles

In contemporary automobiles equipped with electronic control units, "normal" mode refers to the default driving setting that balances engine performance, fuel efficiency, transmission behavior, and ride comfort for typical road conditions. This mode activates standard throttle response, where accelerator pedal input translates to moderate power delivery without aggressive mapping, allowing for responsive yet economical acceleration. Transmission shift points in normal mode prioritize smooth progression through gears at speeds suitable for highway and urban commuting, typically upshifting earlier than in sport-oriented settings to maintain efficiency.^[93]^[94] Suspension and steering assistance in normal mode are calibrated for everyday handling, providing a compliant ride over varied surfaces while ensuring stability during cornering; electronic stability control and traction systems operate at baseline intervention levels without heightened sensitivity found in performance modes. Manufacturers such as Toyota implement normal mode as the factory-preset option upon vehicle startup, reverting to it automatically if no other selection is made, which supports consistent drivability for the average consumer. Ford vehicles similarly use normal mode for standard engine tuning and parameter adjustments, optimizing for general-purpose use without prioritizing extremes in power or parsimony.^[94]^[95] The prevalence of normal mode has grown with the adoption of drive-by-wire systems and programmable ECUs since the early 2010s, enabling drivers to toggle between modes via dashboard selectors or infotainment interfaces; data from automotive analyses indicate that over 70% of mid-2020s compact and midsize sedans and SUVs from major brands include this feature as standard. In electric and hybrid vehicles, normal mode maintains regenerative braking at moderate levels, balancing energy recapture with seamless deceleration akin to internal combustion counterparts. This standardization reflects engineering priorities for versatility, as normal mode accommodates the majority of annual vehicle miles traveled—estimated at 12,000–15,000 per passenger car in the U.S.—without necessitating mode changes.^[96] Beyond drivetrain settings, "normal" in vehicle maintenance contexts denotes operating conditions without excessive stress, such as short trips or dusty environments that trigger "severe" schedules; for instance, oil change intervals extend to 7,500–10,000 miles under normal use per OEM guidelines from brands like those tracked by CARFAX. In fleet and resale evaluations, normal wear encompasses minor cosmetic imperfections like small scratches under 1 inch or interior fading from standard exposure, distinguishing it from abuse-related damage. These definitions underscore "normal" as a benchmark for expected longevity, with vehicles projected to endure 200,000 miles under such parameters when serviced accordingly.^[97]^[98]

Other Transportation Uses

In railway engineering, "normal gauge" designates the standard track gauge measuring 1,435 mm (4 ft 8½ in) between the inner edges of the rails, a configuration used on roughly 60% of the world's rail networks for enhanced interoperability and load stability. Originating from George Stephenson's designs for British collieries and the 1825 Stockton and Darlington Railway, it was codified as the uniform standard in the UK via the 1846 Gauge of Railways Act, influencing global adoption despite regional variations like narrow or broad gauges in parts of Asia, Africa, and Iberia.^[99]^[100]^[101] In aviation regulation, particularly under U.S. Federal Aviation Administration standards, "normal category" classifies small airplanes certified for non-acrobatic operations, excluding intentional spins, rolls, or other maneuvers beyond basic flight attitudes. As defined in 14 CFR Part 23, these aircraft are limited to a maximum certified takeoff weight of 19,000 pounds (updated from prior 12,500-pound thresholds in 2017 amendments) and seating for up to 19 passengers, with airworthiness criteria emphasizing structural integrity for typical utility and transport roles rather than high-performance aerobatics. This category encompasses most general aviation fixed-wing aircraft, distinguishing them from utility, aerobatic, or transport categories based on intended use and load factors.^[102]^[103]

Other Uses

Economics

In economics, a normal good is defined as a commodity or service for which consumer demand rises as real income increases, holding prices constant, resulting in a positive income elasticity of demand greater than zero.^[104] This contrasts with inferior goods, where demand falls with rising income due to substitution toward higher-quality alternatives. Normal goods encompass both necessities (income elasticity between 0 and 1, such as staple foods) and luxuries (elasticity greater than 1, such as high-end electronics), though the term primarily denotes the directional response to income changes rather than quality. Empirical studies, including household expenditure surveys, consistently show this pattern; for instance, demand for restaurant meals and new automobiles typically increases with household income in developed economies.^[105] ^[106] Normal profit, by contrast, represents the minimum return on resources sufficient to maintain a firm in operation in a competitive market, where total revenue equals total economic costs, including both explicit outlays (e.g., wages, materials) and implicit opportunity costs (e.g., forgone returns from alternative investments).^[107] This equilibrium implies zero economic profit, as any supernormal profit would attract entry, eroding returns, while subnormal profit leads to exit. In perfect competition models, long-run equilibrium yields normal profit, ensuring resource allocation efficiency without excess capacity. Accounting profit, which excludes implicit costs, may exceed normal profit, but economic analysis prioritizes the inclusive measure to assess true viability.^[108] For example, a firm earning just enough to cover the owner's next-best alternative salary and capital returns achieves normal profit, signaling sustainability absent barriers to entry.^[109]

Anatomy and Medicine

In clinical medicine, "normal" primarily refers to physiological parameters, laboratory test results, or anatomical features falling within statistically derived reference intervals that represent typical values in healthy populations. These intervals are established by analyzing data from reference groups of at least 120 healthy individuals, excluding those with known diseases, medications, or conditions that could influence outcomes, with the range typically spanning the central 95% of values (from the 2.5th to 97.5th percentiles).^[110] ^[111] For Gaussian distributions, this equates to approximately the mean ± 2 standard deviations, though non-parametric methods are used when data deviate from normality to avoid misclassification of outliers as abnormal.^[112] ^[113] Reference intervals vary by laboratory, test manufacturer, and demographic factors such as age, sex, ethnicity, and pregnancy status, as these influence baseline values; for example, hemoglobin levels differ between adult males (typically 13.5–17.5 g/dL) and non-pregnant females (12.0–15.5 g/dL) due to physiological differences in blood volume and iron stores.^[110] ^[48] Labs may validate or adopt manufacturer-provided ranges but must verify applicability to their local population, as geographic and lifestyle variations can shift norms—e.g., higher altitude residents exhibit elevated hemoglobin due to hypoxia adaptation.^[112] A result outside this range does not automatically indicate pathology, as 5% of healthy individuals fall outside by definition, necessitating clinical correlation with symptoms, history, and trends over time.^[114] In anatomy, "normal" denotes the standard structural configuration and proportions of the human body derived from empirical observations in gross dissection, imaging (e.g., MRI, CT), and population studies, distinguishing typical forms from congenital anomalies or acquired deformities that compromise function.^[115] Normal anatomy encompasses minor variants, such as situs inversus (mirrored organ placement in ~0.01% of people), which are asymptomatic and do not deviate from functional norms, whereas abnormalities like polydactyly or scoliosis exceeding 10–20 degrees curvature are deemed non-normal due to potential biomechanical impairment.^[116] This baseline enables diagnosis of deviations, as in orthopedic assessments where "normal" knee alignment maintains a tibiofemoral angle of 5–7 degrees valgus in adults to optimize load distribution.^[117] Medically, "normal" also applies to interventions mimicking physiological states, such as normal saline (0.9% sodium chloride solution), which is isotonic to plasma (osmolality ~290 mOsm/L) and used for volume resuscitation without disrupting cellular fluid balance, unlike hypotonic or hypertonic alternatives.^[118] The term's application underscores a statistical rather than absolute ideal, as evolving evidence refines ranges—e.g., updated blood pressure norms post-2017 ACC/AHA guidelines lowered "normal" to <120/80 mmHg from prior <140/90 mmHg thresholds based on longitudinal cardiovascular risk data from cohorts like Framingham.^[119]

Computing and Technology

In database design, normalization refers to the systematic organization of data in relational databases to minimize redundancy and dependency, thereby enhancing data integrity and reducing anomalies during insertions, updates, or deletions.^[120] This process, formalized by Edgar F. Codd in his 1970 paper "A Relational Model of Data for Large Shared Data Banks," involves decomposing tables into smaller, related tables that adhere to progressive levels known as normal forms.^[121] The first normal form (1NF) requires that each table cell contains atomic (indivisible) values, with no repeating groups or arrays, and that each record is unique via a primary key.^[122] Second normal form (2NF) builds on 1NF by ensuring that all non-key attributes are fully functionally dependent on the entire primary key, eliminating partial dependencies in composite keys.^[123] Third normal form (3NF) further refines this by removing transitive dependencies, where non-key attributes depend on other non-key attributes rather than directly on the primary key.^[124] Higher forms like Boyce-Codd normal form (BCNF) address certain anomalies in 3NF, while fourth and fifth normal forms handle multi-valued and join dependencies, though practical implementations often stop at 3NF due to performance trade-offs in query efficiency.^[125] In computer graphics, a normal vector is a unit vector perpendicular to a surface at a given point, crucial for algorithms simulating light interaction, shading, and rendering.^[126] These vectors determine how incident light rays reflect or refract, enabling realistic effects in models like the Phong reflection model, where the angle between the normal, light source, and viewer influences diffuse and specular highlights.^[127] For polygonal meshes, vertex normals are often interpolated across faces to compute per-pixel shading, avoiding faceted appearances; normal mapping techniques store perturbation vectors in texture maps to add detail without increasing geometry complexity, as each RGB channel encodes X, Y, Z components relative to the surface tangent space.^[128] Transforming normals under non-uniform scaling requires the inverse transpose of the model matrix to preserve perpendicularity, preventing distortions in lighting calculations during rendering pipelines like those in OpenGL or DirectX.^[127] In theoretical computer science, normal forms denote standardized representations of expressions or terms to facilitate equivalence checking and simplification. For instance, in lambda calculus, normal order evaluation reduces outermost redexes first, aiming for a normal form where no further beta-reductions are possible, aiding in proving termination and confluence properties.^[129] A-normal form, used in compiler intermediate representations, converts programs into a three-address code-like structure with explicit continuations, simplifying optimizations like common subexpression elimination.^[130] These forms prioritize canonical structures over arbitrary equivalents, supporting automated theorem proving and program analysis tools.^[129]

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Anatomy is the identification and description of the structures of living things. It is a branch of biology and medicine.
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What Is Normal? - PubMed
... means that medicine operates without a definition: certain phenomena are normal (by decree, as it were), and others are not. Actions based on such an ...
[120]
The Meaning of Normal - Johns Hopkins University
In many ways, medicine has come to understand normal as a "description of the ideal." Medicine's identification of the normal with the ideal may stem from a.
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What Is Database Normalization? - IBM
Database normalization is a database design process that organizes data into specific table structures. It helps to improve data integrity, prevent data ...What is database normalization? · Importance
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Introduction to Database Normalization - GeeksforGeeks
Oct 9, 2025 · Normalization is an important process in database design that helps improve the database's efficiency, consistency, and accuracy.
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Database normalization description - Microsoft 365 Apps
Jun 25, 2025 · Normalization is the process of organizing data in a database. It includes creating tables and establishing relationships between those tables according to ...
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Database Normalization: 1NF, 2NF, 3NF & BCNF Examples
Jul 26, 2025 · Key Takeaways · Database normalization is a step by step approach to structuring data in a way that reduces redundancy and preserves data ...
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Database Normalization – Normal Forms 1nf 2nf 3nf Table Examples
Dec 21, 2022 · Database normalization is a database design principle for organizing data in an organized and consistent way. It helps you avoid redundancy and maintain the ...
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Normalization in SQL (1NF - 5NF): A Beginner's Guide - DataCamp
May 28, 2024 · Database normalization is a technique that optimally designs the schema of a relational database. It involves dividing tables into smaller ...
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[PDF] 15-462: Computer Graphics
A normal vector is a vector perpendicular to a surface. A unit normal is a normal vector of magnitude one. • Normal vectors are important to many graphics.
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Transforming Normals - Geometry
A surface normal at a point P on a surface is defined as a vector that is perpendicular to the tangent plane at that point.
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Normal Mapping in Computer Graphics - GeeksforGeeks
Jul 23, 2025 · A pixel in a normal map has three channels R, G, and B whose values represent the X, Y, and Z values of the normal vector of that point. For ...
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Normal Forms — Mathematical Foundations of Computer Science
A normal form is a selected representative from a set of equivalent expressions. We use normal forms to convey information in a consistent manner.
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Normal Forms | Core Computer Science - workat.tech
A relation is considered to be in the first normal form if it doesn't contain any multivalued attribute. If all the attributes are single-valued in a table then ...