A pivot is a shaft, pin, or analogous mechanical component that serves as the central axis for the rotation or oscillation of an attached part, as found in devices such as hinges, compasses, and balances.[1] The term derives from Frenchpivot, denoting a small point or pin, with its earliest recorded English usage as a noun in the 14th century.[1] Figuratively, a pivot refers to any person, factor, or element exerting a decisive or central influence on events, outcomes, or dynamics.[1]In sports, particularly basketball, pivoting constitutes a foundational maneuver where a player rotates their body around one stationary foot—the pivot foot—while maintaining control of the ball to evade defenders, survey the court, or position for a shot or pass; improper execution risks a traveling violation.[2][3] This technique underscores balance, spatial awareness, and rule adherence, forming a core skill drilled from youth levels onward.[4]In computing and data analysis, a pivot table functions as a versatile tool for aggregating, reorganizing, and querying large datasets by categories, enabling rapid insights into trends, sums, averages, or counts without altering underlying data; its origins trace to Pito Salas's 1986 invention, with commercial implementations appearing in Lotus Improv (1991) and Microsoft Excel (1993).[5][6] Such tables exemplify efficient computational pivoting on variables, transforming raw inputs into actionable summaries.In entrepreneurship and strategic management, to pivot describes a calculated redirection of a venture's core hypothesis, product focus, or business model in response to empirical validation failures or market signals, without discarding prior validated learnings—a concept formalized and popularized by Eric Ries in his framework of lean startup methodology around 2009.[7][8] This approach emphasizes iterative testing over rigid adherence to initial plans, fostering adaptability amid uncertainty, though it demands rigorous distinction between perseverance on viable paths and timely course correction to avert resource depletion.[9]
Etymology and core definition
Historical origins
The term "pivot" entered English as a noun in the late 14th to early 17th century, denoting a "pin on which a wheel or other object turns," borrowed directly from French.[10][1] The Oxford English Dictionary records its earliest evidence in Middle English from 1398, specifically in the context of mechanical components like hinge pins or shafts enabling rotation.[11]Its French antecedent, pivot, dates to the 12th century in Old French, originally referring to a "hinge pin" or the central turning pin of a wheel, with figurative extensions to a "turning point" even in early usage.[10] The word's precise etymological roots remain uncertain, though it shows parallels with other Romance language terms such as Catalanpiu ("pivot") and Spanishpúa ("sharp point, spike"), suggesting a possible shared Vulgar Latin or pre-Roman substrate origin related to pointed or piercing objects that facilitate pivoting motion.[10] Some linguists propose connections to onomatopoeic or descriptive terms for creaking sounds produced by turning mechanisms, akin to chirping or scraping noises, but no definitive proto-form has been established.[12]By the 1610s, "pivot" had solidified in English technical and mechanical lexicon, appearing in descriptions of artillery, doors, and machinery where rotational stability was key, reflecting its core connotation of a fixed point amid movement.[13] The verb form, meaning "to turn on or as if on a pivot," emerged later in 1841, extending the noun's mechanical sense to actions involving swiveling or reorientation.[10] This evolution underscores the term's grounding in observable physical principles of leverage and rotation, predating abstract or metaphorical applications in later fields like strategy or data analysis.
Fundamental mechanical meaning
In mechanics, a pivot is a short shaft, pin, or fixed point that supports a component enabling it to rotate or turn around an axis while restricting linear motion.[14] This configuration transmits forces primarily as torques, converting applied moments into rotational displacement with minimal frictional losses when properly designed.[1] The pivot's causal role derives from its geometric constraint: it anchors one degree of freedom (rotation) while immobilizing others (translation), a principle observable in basic rigid-body dynamics where equilibrium requires balancing moments about the pivot axis.[15]Pivots differ from sliding bearings or universal joints by permitting uniaxial rotation, often under load, as seen in clock mechanisms where jeweled pivots reduce wear on balance wheels rotating at frequencies up to 10 Hz in precision timepieces.[14] In lever systems, the pivot serves as the fulcrum, amplifying input force via lever arm ratios; for instance, a class-1 lever pivots between load and effort points, achieving mechanical advantages exceeding 5:1 in tools like crowbars.[16]Friction at the pivot interface, modeled as Coulombic with coefficients typically 0.05–0.15 for lubricated steel-on-steel contacts, must be minimized to prevent energy dissipation and ensure precise control.[17]Engineering analyses treat pivots as ideal points for torque calculations in statics, where the resultant force at the pivot equals the vector sum of external loads to maintain zero net translation.[18] Real-world implementations incorporate materials like hardened steel or ceramics to withstand shear stresses up to 500 MPa, with historical refinements dating to 17th-century horology emphasizing low-inertia designs for oscillatory pivots in pendulums.[14] This fundamental setup underpins rotational kinematics, where angular acceleration \alpha relates to net torque \tau via \tau = I \alpha, with I as the moment of inertia about the pivot.[19]
Physical and biological applications
Pivot in mechanics and physics
In mechanics, a pivot is a fixed point or axis that constrains the motion of a rigid body, allowing rotation about that point while preventing translation. This concept is fundamental to analyzing rotational systems, where the pivot serves as the reference for torque calculations, defined as \tau = r \times F, with r being the perpendicular distance from the pivot to the line of action of force F.[20] In static equilibrium problems, the pivot point is chosen arbitrarily to simplify equations, as the net torque about any point must sum to zero for balance, enabling the resolution of unknown forces without requiring the pivot's reaction force to appear in the torque sum.[21] For instance, in a seesaw or lever, the pivot (fulcrum) supports the beam, and equilibrium occurs when clockwise and counterclockwise torques balance, as governed by the principle that the product of force and lever arm equals on both sides.[22]In physics, particularly rotational dynamics, the pivot defines the axis for angular acceleration and inertia. An object's moment of inertia I about the pivot influences its response to applied torques via Newton's second law for rotation, \tau = I \alpha, where \alpha is angular acceleration.[20] Pivots appear in everyday mechanical systems like door hinges, where frictional resistance at the pivot affects rotational ease, or in pendulums, where the suspension point acts as the pivot for oscillatory motion under gravity.[23] In non-equilibrium scenarios, such as a bat striking a ball, the pivot may align with the center of percussion—a point where an impulse produces no reaction torque at the handle—to minimize vibrational stress.[21] The choice of pivot is physically invariant; shifting it requires adjusting for parallel axis theorem, I = I_{cm} + md^2, where I_{cm} is the moment about the center of mass and d the distance to the new pivot.[22]Pivots also feature in constrained systems, such as linkages in machinery, where multiple pivots enable complex motions while transmitting forces efficiently. Experimental verification often involves torque balances, as in Cavendish's 1798 torsion balance for measuring gravitational constant G, where a pivoted beam twists under mutual attraction of masses.[20] In advanced applications, like gyroscopes, the pivot allows precession under torque, demonstrating conservation of angular momentum. These principles underpin engineering designs, from bridges resisting pivot-induced moments to robotic arms optimizing pivot placements for stability.[23]
Pivot joint in anatomy
A pivot joint is a uniaxial synovial joint that permits rotational movement around a single axis, with one articulating surface rotating relative to a stable ring-like structure formed by bone and ligaments.[24][25] In this arrangement, a cylindrical or peg-like bony process fits into a concavity or ring, enabling trochoid (wheel-like) motion while limiting translation.[24] These joints are classified under the six types of synovial joints, distinguished by their capacity for rotation without significant gliding or hinging.[25]Structurally, pivot joints feature a synovial capsule enclosing the articulation, with articular cartilage covering the moving surfaces to reduce friction during rotation; surrounding ligaments provide stability against dislocation.[24] The joint's design relies on precise bony geometry and ligamentous reinforcement, such as the annular ligament, to constrain motion to pure rotation and prevent axial slippage.[26] Blood supply derives from adjacent regional arteries, while innervation supports proprioception and reflex arcs.[24]Functionally, pivot joints contribute to essential rotational freedoms in the axial and appendicular skeletons, accounting for specific degrees of freedom in compound movements like cervical rotation or forearm twisting.[27] Motion is limited to approximately 90 degrees in many cases, depending on ligament tautness and muscular control, with synovial fluid lubricating the interface to minimize wear.[25]Prominent examples include the median atlantoaxial joint, where the dens (odontoid process) of the axis (C2vertebra) pivots within the anterior arch and transverse ligament of the atlas (C1), facilitating 40-50% of total head rotation (up to 47 degrees per side).[26][28] Another is the proximal radioulnar joint, in which the radial head rotates within the ulnar radial notch and annular ligament, enabling forearm pronation and supination through a 150-180 degree arc.[29] The distal radioulnar joint mirrors this mechanism distally, coordinating with the proximal for coupled forearm rotation.[29] These joints underscore the body's reliance on specialized articulations for precise, low-friction rotary tasks.[24]
Mathematics and computing
Pivot element in linear algebra
In the context of linear algebra, a pivot element, also known as a pivot entry, is a specific nonzero entry in a matrix that serves as the leading coefficient in a row during the process of Gaussian elimination or row reduction to achieve row echelon form.[30] This element is typically positioned at the top of the leftmost nonzero column in the current submatrix and is used to eliminate entries below it in the same column, facilitating the transformation of the matrix into an upper triangular form.[31] The pivot is often scaled to 1 through row operations, ensuring it becomes the leading 1 in its row of the echelon form.[32]Pivot positions are the locations of these leading entries in the reduced row echelon form of the matrix, which uniquely determine the rank of the matrix as the number of such positions.[33] Columns containing pivot positions, termed pivot columns, correspond to linearly independent columns of the original matrix and form a basis for its column space.[34] Non-pivot columns indicate free variables in the solution set of associated linear systems, influencing the dimension of the null space via the rank-nullity theorem.[30]For numerical stability in computations, especially with floating-point arithmetic, pivoting strategies select the pivot element strategically: partial pivoting chooses the largest absolute value in the current column below the diagonal to minimize error growth, while complete pivoting selects the global maximum in the remaining submatrix.[35] These techniques bound the growth factor—the ratio of the largest element post-elimination to the original maximum—preventing exponential error amplification, as demonstrated in analyses of LU decompositions without pivoting leading to instability in ill-conditioned matrices.[36] In exact arithmetic over fields like rationals, pivots simply ensure nonzero selection via row swaps if needed, but in practice, they are essential for reliable algorithmic implementation in software like MATLAB or NumPy.[37]
Pivot tables in data analysis
Pivot tables, also known as PivotTables in software like Microsoft Excel, are interactive data summarization tools that enable users to rearrange, aggregate, and analyze large datasets dynamically without requiring programming or complex formulas.[38] They transform raw tabular data—such as sales records or survey responses—into customizable views that reveal patterns, trends, and comparisons by grouping values across rows, columns, and filters.[39] For instance, a pivot table can sum revenue by product category and region while filtering for a specific year, updating results in real-time as fields are dragged and dropped.[40]The concept originated in 1986 from Pito Salas, who developed the idea of flexible data views during his work on spreadsheets, with initial implementation in Lotus Improv in 1991 and integration into Microsoft Excel version 5.0 in 1993.[6] This timeline marked a shift from static spreadsheets to dynamic analysis, allowing non-experts to perform operations like counting occurrences, averaging metrics, or calculating percentages across multidimensional data.[41] By 2023, Excel's pivot tables had evolved to handle millions of rows via integration with Power Pivot, supporting data models from multiple relational tables.[42]In operation, pivot tables rely on four primary areas: rows for categorical breakdowns (e.g., by department), columns for cross-tabulation (e.g., by quarter), values for aggregations (e.g., sum of sales using functions like SUM, COUNT, or AVERAGE), and filters or slicers for subsetting data.[43] Users select a source range or table, then configure these areas to generate summaries; for example, from a dataset of 100,000 transactions, a pivot table might produce a report showing average order value by customer segment in seconds.[44] Advanced features include calculated fields for custom metrics (e.g., profit margin as revenue minus costs) and grouping for hierarchies like date rollups into months or years.[39]Common applications in data analysis include exploratory analysis of business metrics, such as identifying top-performing products or detecting seasonal trends in inventorydata.[40] They facilitate rapid prototyping of reports, reducing manual aggregation errors and enabling what-if scenarios by refreshing against updated sources.[6] Limitations arise with very large datasets exceeding memory constraints or non-tabular inputs, often mitigated by tools like Power Query for preprocessing.[45] Overall, pivot tables democratize data insights, proving effective for ad-hoc queries in fields from finance to marketing without necessitating statistical software.[46]
Business and economics
Strategic pivot in startups and entrepreneurship
A strategic pivot in startups refers to a deliberate change in a company's direction, such as altering its product features, target market, or business model, while preserving validated learnings and core vision from prior efforts.[8] This concept was formalized by entrepreneur Eric Ries in his 2011 book The Lean Startup, where he described it as a structured process to test new hypotheses about growth engines after empirical evidence indicates the original strategy is not achieving product-market fit. Pivots are grounded in iterative experimentation, often triggered by metrics like stagnant user growth or poor retention rates, rather than arbitrary shifts.[47]Pivots typically arise from causal factors such as failure to penetrate the intended market, excessive competition, or unexpected customer behaviors revealing untapped opportunities.[48] For instance, founders may pivot when internal data shows the product solving a different problem than anticipated, or when external market dynamics, like technological disruptions, render the initial approach obsolete.[49] Unlike a full reboot, a pivot leverages sunk costs in technology or user insights to minimize risk, emphasizing causal realism by building on proven elements like reusable codebases or audience data. Empirical analysis from venture-backed firms indicates that pivots are most effective when limited to 1-2 iterations, correlating with 3.6 times higher user growth and 2.5 times more funding raised compared to non-pivoting or excessively pivoting startups.[50]Notable examples illustrate successful pivots driven by market feedback. Twitter originated as Odeo, a podcasting platform struggling after Apple's 2005 iTunes dominance, prompting a 2006 shift to short-message broadcasting among employees, which evolved into the core microblogging service.[51]Slack emerged from Tiny Speck's 2012 multiplayer game Glitch, which failed to gain traction; the team's internal communication tool, built atop the game's infrastructure, pivoted to enterprise messaging and launched in 2013, achieving rapid adoption.[52]Instagram began as Burbn, a 2010 location-based check-in app with photo-sharing features, but user data showed preference for the photo component, leading to a pivot that stripped extraneous elements and focused on filters and social feeds, resulting in 1 million users within months of its October 2010 relaunch.[51]Data on pivot outcomes underscores their role in entrepreneurship, with approximately 70% of startups undergoing at least one pivot, and 93% of ultimately successful ones reporting pivots as key to refinement.[53][54] However, pivots do not guarantee success; overall startup failure rates remain high at over 90% long-term, often due to poor execution or ignoring deeper causal issues like flawed team dynamics rather than the pivot itself.[55] Effective pivots require rigorous validation through metrics, distinguishing them from reactive desperation, and are more prevalent in tech sectors where low marginal costs enable rapid testing.[56]
Pivot points in financial trading
Pivot points are technical analysis indicators employed by traders to anticipate potential intraday support and resistance levels in financial markets, including stocks, forex, and futures. Derived from the prior trading session's high, low, and closing prices, they provide objective price targets for entry, exit, and reversal points. The central pivot point serves as a baseline, with additional resistance (R) and support (S) levels calculated above and below it, respectively, to gauge market sentiment: prices trading above the pivot suggest bullish conditions, while those below indicate bearish trends.[57][58]The standard pivot point formula, originating from early 20th-century floor traders, uses the arithmetic mean of the previous period's high (H), low (L), and close (C):
These are typically computed using daily data for intraday trading, though weekly or monthly periods apply for longer horizons.[59][57]Developed by exchange floor traders in the 1930s to anticipate price movements amid high-volume pit trading, pivot points gained prominence for their simplicity and reliance on prior session extremes, reflecting collective market memory without subjective interpretation.[57] Variations emerged over time, including Fibonacci pivots, which incorporate Fibonacci ratios (e.g., R1 = P + 0.382 × (H - L)) for levels aligned with natural price retracements; Woodie's method, emphasizing the close price (P = (H + L + 2 × C)/4); Camarilla equations for tighter intraday ranges; and DeMark's predictive variant, using conditional highs/lows based on open-close relationships. Each suits different assets and volatilities, with standard pivots favored in forex due to 24-hour liquidity.[60][61]Traders apply pivot points by monitoring price interactions: bounces off support/resistance signal continuations, while breaks validate trend shifts, often combined with volume or candlestick confirmation to filter false signals. For instance, a long entry might trigger above R1 with rising volume, targeting R2, or a short below S1 aiming for S2. In practice, they excel in ranging markets but falter in strong trends, where prices ignore levels.[62][63]Empirical assessments reveal limited standalone efficacy. Backtests on U.S. stocks show pivot-based strategies underperform buy-and-hold in 67% of cases on hourly charts and 94% on five-minute intervals, attributing this to self-fulfilling prophecy from widespread use rather than inherent predictive power. Academic reviews of technical analysis, including pivots, find mixed results, with profitability sensitive to transaction costs, slippage, and market regime; while some forex studies report modest edges in high-liquidity pairs, overall evidence suggests no consistent alpha generation beyond efficient market benchmarks.[64][65][66]
Sports and athletics
Pivot move in basketball
The pivot move in basketball constitutes a core footwork technique employed when a player, upon receiving the ball while stationary, designates one foot as the pivot foot—which remains planted on the floor—and rotates the body around it using the other foot to alter direction, shield the ball, or position for a shot, pass, or drive.[2] This maneuver enables players to maintain legal possession without dribbling, provided the pivot foot does not lift or drag before the ball is released.[67] In official rules, such as those of the NBA, a player catching the ball with both feet on the floor may select either as the pivot; alternatively, the first foot to touch the floor after gathering the ball establishes the pivot, with the other foot free to move.[68] Violating this by relocating the pivot foot without initiating a dribble, pass, or shot results in a traveling violation, forfeiting possession to the opposing team.[68]Executed properly, the pivot facilitates deceptive movements, such as faking a drive before pulling up for a jump shot or backing down a defender in the post.[67] Players often adopt a triple-threat stance—ball held in one hand at chest level, knees bent, and body squared—prior to pivoting, which allows seamless transitions to shooting, passing, or dribbling.[2] Forward pivots turn the body away from the defender to open passing lanes, while reverse (or inside) pivots rotate toward the baseline, effectively sealing opponents or creating separation for hooks or fades.[69] Mastery of pivoting demands balance, core strength, and awareness of the pivot foot's establishment, particularly off the dribble where the gathering foot becomes the pivot upon stopping.[69]Historically, the pivot has anchored post play since basketball's formative years, with George Mikan exemplifying the "pivot man" archetype in the 1940s and 1950s by positioning low near the basket, catching entry passes, and pivoting against smaller defenders for close-range scores.[70] The reverse pivot, less common initially, emerged as a counter to aggressive fronting defenses, popularized by forwards like Jack Sikma in the NBA from 1977 to 1991, who used it to exploit mismatches and contribute to Seattle SuperSonics' contention, earning seven All-Star selections.[71] Modern players, including Tim Duncan—who frequently pivoted into bank shots during his 19 NBA seasons—and Kobe Bryant, integrated pivots into versatile isolation scoring, enhancing efficiency in high-stakes possessions.[67] Coaching emphasizes early pivot training to instill discipline, reducing traveling calls that plagued youth and amateur levels, where improper footwork accounts for frequent turnovers.[2]
Pivots in other sports
In association football (soccer), the term "pivot" denotes a defensive midfielder or deep-lying playmaker positioned to link the defense with the rest of the midfield, shielding the backline while facilitating ball distribution and tempo control. This role demands strong positional awareness, passing accuracy, and tackling ability to intercept opposition advances and initiate counters. A double pivot employs two such players in formations like the 4-2-3-1, providing numerical superiority in midfield battles, as exemplified in teams such as Bayern Munich under coaches emphasizing structured build-up play.[72]In ice hockey, pivoting refers to a fundamental skating technique for transitioning direction, particularly from forward to backward skating, crucial for defenders maintaining gap control and body positioning against attackers. The maneuver involves quick foot rotation on edges while preserving speed and balance, often executed via a mohawk turn where heels nearly touch to open hips efficiently. Defensemen practice pivots extensively to cover zones, evade forechecks, and support rushes, with variations like backward-to-forward pivots enabling seamless offensive transitions.[73][74]Volleyball setters employ pivoting as a footwork pattern to adjust positioning for accurate sets, such as the right-foot pivot generating torque for back sets or out-of-system passes. This involves rotating on the pivot foot to align shoulders toward targets while maintaining balance, essential for quick releases under pressure from medium or erratic receives. Techniques like the pivot step allow setters to extend their range without losing momentum, improving set precision in competitive play.[75]In boxing, the pivot is a defensive footwork maneuver where a fighter rotates on the lead foot to alter angles, evade punches, and set up counters like the pivot hook. Executed from an orthodox stance, it shifts body position rapidly while keeping the rear foot free for power generation, emphasizing balance and timing to avoid telegraphing movements. Professional bouts highlight pivots for creating offensive openings, as seen in tutorials breaking down its role in maintaining distance and unpredictability.[76]
Linguistics and language
Pivot in syntactic theory
In syntactic theory, particularly within typological and functionalist frameworks, the pivot denotes the core grammatical relation that governs argument selection and linkage across clauses in constructions such as coordination, relativization, and control. This relation privileges one or more of the primary arguments (intransitive subject S, transitive agent A, or transitive patient O) as the structural "hub" around which syntactic operations revolve, enabling coreference or omission without full NP realization in subordinate clauses. For instance, in languages with an S/A pivot, the subject of an intransitive verb and the agent of a transitive verb behave uniformly, allowing either to serve as the pivot for processes like subject-to-subject raising or equi-NP deletion.[77]Pivots contrast with purely semantic alignments by reflecting language-specific syntactic equivalences rather than universal thematic roles, as evidenced in ergative languages where an S/O pivot treats the intransitive subject and transitive object as equivalent for cross-clausal linkage. R.M.W. Dixon formalized this in analyses of Dyirbal, an Australian language, where much of the syntax hinges on S/O pivots: in purposive clauses or instrumentals, the transitive object or intransitive subject must be zeroed or pronominalized to match the pivot role in the main clause, while the transitive agent requires a separate antipassive derivation for pivot compatibility. This S/O pattern yields syntactic ergativity, distinct from morphological ergativity, as pivots dictate accessibility hierarchies in relativization and coordination—e.g., S or O can be relativized without voice adjustment, but A cannot. Dixon's 1979 framework, building on earlier work, posits pivots as diagnostic for grammatical relations, with empirical support from over 100 languages showing pivot-choice correlates with case-marking typology but not strictly determined by it.[78]Pivot theory extends to mixed systems and diachronic shifts, where languages may exhibit pivot splits conditioned by tense-aspect (e.g., S/A in past tenses, S/O in future) or hierarchy effects prioritizing higher animacy arguments. In Role and Reference Grammar, pivots integrate with macroroles (Actor and Undergoer) to model clause linkage, treating the pivot as the unmarked choice for semantic-semantic pivoting in ergative-dominant languages. Critiques note that pivot behaviors can overlap with pragmatic topic prominence, yet cross-linguistic data affirm their syntactic autonomy, as in Philippine languages where the S/A pivot (often termed "topic" or "focus") enforces voice alternations to promote non-pivot arguments. Empirical validation relies on controlled elicitations and corpus analyses, revealing pivots' role in constraining ellipsis and anaphora beyond linear order or prosody.[79]
Arts and music
Pivot chord in harmony
A pivot chord in tonal harmony is a chord that belongs diatonically to both the original key and the target key during a modulation, enabling a seamless transition by functioning simultaneously in both tonal contexts.[80][81] This technique, known as pivot chord modulation or common chord modulation, relies on the shared chord's dual harmonic roles to pivot from one key to another without abrupt disruption.[82] The pivot chord typically appears at the point of overlap in the progression, often analyzed by its Roman numeral function in each key—for instance, as a predominant or subdominant in the original key and tonic or dominant in the new key.[80]Pivot chords facilitate modulations to closely related keys, such as the dominant (up a fifth), relative minor, or mediant, where diatonic overlap is most feasible.[81] To identify a suitable pivot, composers select a chord diatonic to both keys, positioning it strategically within a phrase to maintain forward momentum; for example, modulating from C major to G major might use the D minorchord (ii in C major, vi in G major).[80] In practice, the pivot often precedes a strong cadence in the new key, such as a V–I progression, to confirm the modulation.[83] This method contrasts with abrupt modulations (e.g., via enharmonic reinterpretation) by preserving continuity through shared pitch content.[82]Diatonic pivot chords involve unaltered common tones from both keys' scales, ensuring smooth voice leading.[80] Chromatic pivot chords, however, incorporate borrowed or altered elements, such as mode mixture, where the pivot functions diatonically in one key but chromatically in the other (e.g., a flat-VI chord borrowed from the parallel minor serving as a pivot to the relative major).[84] For modulations to distantly related keys, altered pivot chords may substitute, like a secondary dominant reinterpreted enharmonically, though this borders on non-pivotal techniques.[82]Common examples include modulating from C major to A minor using A minor as the pivot (vi in C, i in A minor), establishing the relative minor via its tonic function post-pivot.[85] Another frequent case is from C major to E minor (iii in C to i in E), pivoting on E minor itself.[81] In jazz and popular contexts, seventh chords expand options, such as F7 as IV7 in C major pivoting to ii7 in B-flat major.[83] These structures underpin much of Western tonal composition from the Baroque era onward, as analyzed in pedagogical texts on harmony.[80]
Geography and places
Settlements named Pivot
Pivot is a small hamlet (hameau) situated within the commune of Provinois, in the Seine-et-Marne department of the Île-de-France region, France.[86][87] The locality lies south-west of the main village of Villars in the Provinois area, amid agricultural lands and forests extending from the Brie plain.[87] Archaeological surveys near the hamlet have revealed pottery fragments, indicating historical human activity, though no specific dating or cultural attribution has been widely documented.[88]As a minor rural settlement, Pivot lacks independent administrative status and detailed demographic records; it forms part of Provinois, which had a population of approximately 300 residents as of recent censuses, though the hamlet itself supports few permanent inhabitants.[87] The name may derive from local topography or historical features, but etymological origins remain unverified in available sources. No significant modern infrastructure or events are associated with the site, which blends into the surrounding countryside used for hiking and limited agriculture.[88]
Organizations and media
Companies using Pivot
Several prominent technology companies have employed the pivot strategy, fundamentally altering their business models in response to market feedback, technological shifts, or competitive pressures to achieve greater success. A pivot involves a structured change in one or more core elements, such as target audience, product features, or revenue model, while retaining validated aspects of the original venture.[89] This approach, popularized in startup lore by Eric Ries in his 2011 book The Lean Startup, emphasizes iterative testing over rigid adherence to initial plans.[47]PayPal, originally launched as Confinity in 1998, focused on security software for handheld devices like Palm Pilots but pivoted in 1999 to email-based payments after user demand for peer-to-peer transfers surged during the eBay boom; this shift enabled rapid scaling, culminating in its 2002 acquisition by eBay for $1.5 billion.[90] Similarly, Netflix began as a DVD-by-mail rental service in 1997, charging late fees that frustrated customers, but pivoted to streaming in 2007 amid broadband proliferation, investing $100 million initially and growing to over 200 million subscribers by 2023 through original content production.[91][92]Twitter originated as Odeo, a podcasting platform founded in 2005, but pivoted to microblogging in 2006 after Apple's iTunes dominated podcast distribution; the internal hackathon project "Twttr" emphasized 140-character status updates, attracting 300,000 users within two months and evolving into a global social media network valued at $44 billion upon its 2022 acquisition by Elon Musk.[93]Slack started as Tiny Speck in 2009, developing a multiplayer game called Glitch, but pivoted in 2013 to commercialize its internal team communication tool after the game's underperformance, reaching 15,000 paying customers within a year and selling to Salesforce for $27.7 billion in 2020.[90] These cases illustrate how pivots, grounded in customer data and rapid prototyping, can transform near-failures into industry leaders, though success rates remain low—estimated at under 20% for startups attempting major shifts—due to execution risks and market timing.[94]
Pivot is a podcast co-hosted by technology journalist Kara Swisher and New York University marketing professor Scott Galloway, offering commentary on developments in technology, business, and politics.[95] Episodes air twice weekly on Tuesdays and Fridays, typically lasting 45 to 60 minutes, and feature discussions on current events such as artificial intelligence advancements, corporate mergers, and policy impacts on industry.[96] The program emphasizes candid analysis, often critiquing corporate leadership and regulatory failures, drawing on the hosts' expertise in media and academia.[97]Launched on September 24, 2018, Pivot initially operated independently before partnering with New York Magazine in April 2020 and integrating into the Vox Media Podcast Network, which expanded its distribution and production resources.[98][99] By 2021, Vox Media broadened the collaboration to include video content and live events, culminating in a 2025 live tour announced for November with stops in Washington, D.C., Brooklyn, and Los Angeles.[100][101] The podcast has accumulated over 700 episodes as of 2025, maintaining a listener base evidenced by more than 8,000 ratings averaging 4.2 on Apple Podcasts.[96]Swisher, a veteran reporter with experience at The Wall Street Journal and as editor-at-large for New York Magazine, brings insider perspectives on Silicon Valley dynamics, while Galloway provides data-driven economic forecasts and critiques of big tech monopolies through his "Prof G" brand.[102] Notable guests have included Meta CEO Mark Zuckerberg and various industry executives, with episodes addressing topics like OpenAI's Sora model and potential government shutdowns.[96][103] The format avoids scripted interviews in favor of debate-style exchanges, which Galloway has described as aimed at dissecting power structures without deference to industry narratives.[104]Pivot has received recognition, including Webby Awards for business content, reflecting its influence in tech discourse amid broader skepticism toward mainstream media's coverage of innovation.[97] Critics, however, note the hosts' occasional alignment with progressive policy views, such as antitrust measures against tech giants, which may color interpretations of market failures over structural incentives.[105] Despite this, the podcast's reliance on verifiable industry data and host disclosures of conflicts—such as Galloway's investments—supports its analytical rigor.[103]
Politics and policy
Policy or electoral pivot
A policy or electoral pivot refers to a strategic reconfiguration of a political candidate's messaging, issue prioritization, or occasionally substantive positions following the primary phase of an election campaign, aimed at broadening appeal to moderate, independent, or opposing-party voters in the general election. This tactic is particularly prevalent in multi-stage electoral systems like the United States, where primaries incentivize appeals to partisan bases through heightened ideological rhetoric, necessitating a subsequent shift toward pragmatism or economic focus to capture swing constituencies. Pivots typically emphasize de-emphasizing polarizing topics—such as cultural wedge issues—in favor of unifying themes like fiscal responsibility or national security, though they rarely entail wholesale reversals of core beliefs.[106][107]The practice draws scrutiny for potentially undermining authenticity, as abrupt changes can appear opportunistic and fuel accusations of hypocrisy, eroding public confidence in politicians' convictions. Empirical analysis of voter behavior indicates that successful pivots correlate with improved general election polling among undecideds, but failures—often due to inconsistent execution or media amplification of contradictions—can reinforce perceptions of insincerity. Mainstream coverage, frequently from outlets with institutional leanings toward critiquing conservative pivots more harshly, highlights this tension, though data from election post-mortems affirm the structural incentives driving such maneuvers regardless of party.[108][109]In the 2012 Republican presidential primaries, Mitt Romney exemplified a textbook pivot upon clinching the nomination. After decisive wins on April 3, 2012, in Wisconsin (capturing 42% of the vote), Maryland (66%), and the District of Columbia (72%), Romney declared the intra-party contest concluded and refocused his campaign on President Barack Obama's handling of the sluggish post-2008 recovery, including unemployment rates hovering above 8%. This shift de-emphasized social conservatism, which had dominated primary debates, to underscore Romney's business credentials and economic reform agenda, aiming to consolidate 2012's median voter.[110][111]Donald Trump's 2016 Republican bid tested the limits of post-primary adaptation. Advisors urged a pivot away from primary-era bombast on immigration and trade deficits—rhetoric that galvanized the base but alienated suburban moderates—to a more disciplined, policy-oriented approach. In early September 2016, Trump reduced arena rallies (from an average of several per week to just two in the month's first eight days) in favor of targeted town halls and economic messaging, yet polls showed minimal gains, with his unfavorability ratings exceeding 55% in national surveys; he largely reverted to base-mobilizing tactics, contributing to a narrow Electoral College victory despite losing the popular vote by 2.1 percentage points.[112][107]A stark instance of positional adjustment occurred in the 2022 New Hampshire Senate race, where Republican nominee Don Bolduc, after winning the September 13 primary with 59% of the vote amid claims that the 2020 presidential election was stolen, pivoted two days later by acknowledging Joe Biden's legitimate victory and accepting certified results. This reversal sought to neutralize Democratic attacks in a swing state where independents comprised 40% of voters, though Bolduc ultimately lost to incumbent Democrat Maggie Hassan by 9 points on November 8, 2022.[113]Policy pivots by incumbents or governing parties similarly adapt to electoral pressures, such as the post-election fiscal recalibrations observed in parliamentary systems. In the United Kingdom following the 2023 general election, incoming Labour leadership signaled a pivot from campaign-era spending restraint to baseline-setting budget expansions, leveraging majoritycontrol to redefine fiscal parameters for long-term policyimplementation. Such shifts underscore causal dynamics where electoral mandates enable pragmatic deviations from pre-vote platforms, prioritizing governability over rigid ideology.[114]