4Edit
The number 4 is a fundamental element of arithmetic and everyday counting. In the decimal system, it is written with a single digit and occupies a stable place between 3 and 5. Mathematically, 4 is the smallest positive composite number and the second square number, being equal to 2 (number)^2. Its status as an even, highly structured figure makes it a recurring unit in a wide range of disciplines, from algebra and geometry to computing and measurement. In everyday life, 4 appears as a core organizing principle: the year’s seasons, the four compass directions, and many culturally significant groupings rely on fours as a tidy, repeatable framework.
The cultural footprint of 4 is as broad as it is enduring. In many Western and global traditions, the number underpins the idea of balance and completeness: a fourfold set of seasons, a four-point cardinal system, and a square or quadrilateral geometry built from four sides and four angles. In religion and literature, there are notable quartets such as the four Gospels and, in Buddhist thought, the Four Noble Truths. In popular culture, the notion of a “quartet” recurs in everything from literature to comic books, with titles like The Fantastic Four illustrating how a four-person team can symbolize a complete unit. In East Asia, the cultural resonance of 4 is more nuanced: the practice of avoiding the fourth floor in buildings, a phenomenon known as Tetraphobia, stems from phonetic associations of the character for “four” with death in some languages, illustrating how numerals can influence architecture and commerce without altering the underlying mathematics.
From a policy and governance perspective, fours often appear as a convenient cadence for accountability and reform. A large portion of government and corporate leadership in many countries is structured around four-year terms or four-year planning cycles, providing a predictable horizon for budgets, policy implementation, and electoral accountability. The stability implied by such cycles aligns with a preference for durable institutions and tested procedures, while still allowing regular renewal through elections or leadership transitions. The same structural logic informs the use of four quarters in fiscal and reporting calendars, a convention that supports clarity, comparability, and prudent stewardship.
Mathematical properties
Arithmetic and divisibility
4 is the product of two and itself, 2×2, which makes it the smallest positive composite number. Its divisors are 1, 2, and 4. Because it is even, it lies on the even-number line that begins with 2, 4, 6, and so forth, and it serves as a basic reference point in modular arithmetic and divisibility tests. See also composite number and even number.
Representation in numeral systems
In the decimal or base-10 system, 4 is written with a single digit. In the Roman numeral system, it is represented as IV, a form of subtractive notation used in classical inscriptions. In binary, the value is 100. This multiplicity of representations illustrates how a single quantity can be encoded in different symbolic systems. See Roman numerals and binary numeral system for more detail.
Geometry and computation
As a square number (2^2), 4 is the cornerstone of many geometric constructions and proofs. The square has four equal sides and four right angles, a basic figure in plane geometry. In computation and data, 4 underpins ideas like grouping in fours, grid structures, and periodic patterns in algorithms (for example, mod 4 arithmetic, which is important in certain hashing and bitwise operations). See square (geometry) and modulo operation for related discussions.
Cultural significance and symbolism
In the Western tradition
The number 4 frequently appears as a sign of completeness and symmetry: four seasons mark the cycle of the year, and four directions give a frame for navigation. The idea of a fourfold division is echoed in literature and art as a means of organizing thinking and space.
In religion and philosophy
Quartets recur in sacred texts and doctrine: the four Gospels present the life of Gospels from four vantage points, while in Buddhism the Four Noble Truths outline a core pathway to enlightenment. These quartets are often invoked to emphasize balance, law, and moral structure in human life.
In East Asia and other cultures
Tetraphobia highlights how numbers can be charged with cultural meaning beyond mathematics. Some people and businesses avoid the fourth floor or other uses of the number 4 to respect local sensitivities and avoid misfortune, even as the mathematical meaning of 4 remains unchanged. See Tetraphobia for an overview of the cultural dimensions.
In art, games, and sport
Fours appear in compositions, storytelling, and competition: a four-person team can symbolize unity and completeness (as in The Fantastic Four), and many sports use four quarters to allocate play time and scoring. The ubiquity of four in games and narratives reinforces its role as a dependable, widely understood unit.
Language and scripts
The digit 4 is one of the most common numerical symbols encountered in everyday writing and mathematics, linking spoken language to abstract quantity. Across inscription systems, from Roman numerals to digital encodings, the same quantity is carried by different signs, reflecting the interplay between culture, technology, and arithmetic. The simplicity and stability of a single-digit symbol in base-10 help ground commerce, accounting, and education in a familiar, repeatable unit.