Flip
Flip is an English verb denoting the action of tossing or propelling an object with a sudden sharp movement so as to cause it to turn over or spin in the air, as exemplified by flipping a coin for decision-making or flipping a pancake during cooking.[1] The term also functions as a noun referring to such a toss or to a somersault performed in gymnastics or acrobatics, and informally as an interjection expressing mild annoyance or surprise.[1] Originating in the early 17th century, likely as an alteration of flap or imitative of the sound of a quick motion, "flip" has evolved to convey casual impudence in phrases like "flip attitude," though its core usage remains tied to physical inversion or reversal.[1] In technical contexts, such as computing or engineering, "flip" describes inverting binary states (e.g., flipping a bit from 0 to 1) or mirroring images, underscoring its broader connotation of reversal.[2]Linguistic and general usage
Verb meanings and etymology
The verb flip emerged in the late 16th century, primarily denoting a quick flick or toss executed with the thumb or fingers, akin to a fillip—a snapping motion attested since the mid-15th century—or formed imitatively to evoke the sharp sound and abrupt movement involved.[3] [4] Its earliest recorded intransitive use, meaning to make a flicking motion, dates to 1565, while transitive applications for striking or propelling with a finger appear by 1594.[4] This origin reflects the physical causality of imparting rotational force through a precise, impulsive gesture, distinguishing it from mere throwing by emphasizing inversion or spin.[1] A foundational sense is to propel an object with a sudden snap, causing it to rotate end-over-end in the air, as in tossing a coin to resolve a binary choice, with evidence of this practice from 1661.[4] Closely related is the transitive use to invert or reverse the position of an object via a brisk motion, such as turning over a pancake on a griddle to ensure even cooking, rooted in the same kinetic principle of leverage and momentum.[1] These usages underscore empirical mechanics: the thumb's leverage generates torque, reliably producing aerial rotation or surface inversion when applied to lightweight, symmetric items like coins or thin foods.[1] In colloquial English, particularly from the mid-20th century, flip extends metaphorically to abrupt attitudinal or emotional reversals, as in "flipping one's attitude" or the idiomatic "flip one's lid" (to suddenly lose self-control), first documented in 1949.[3] [4] This slang evolution draws analogically from the verb's core physical unpredictability—much like a coin's random landing after spin—to describe volatile human shifts, though without the deterministic physics of literal tossing.[1]Noun meanings in everyday contexts
In everyday language, the noun "flip" denotes an instance of a quick toss or turn, such as the act of propelling an object like a coin into the air to determine a random outcome, where the result is the side facing up upon landing.[5] This usage emphasizes the concrete event or its static endpoint, distinct from the verb form, as in resolving disputes by observing whether the coin shows heads or tails after the toss.[6] The term also refers to a rapid bodily rotation, synonymous with a somersault, particularly in casual settings like playground activities or informal gymnastics where an individual performs an aerial turnover without equipment.[5] Such flips involve the body executing a complete revolution, often forward or backward, landing on the feet, as commonly seen in children's play or basic acrobatics.[7] Associated objects include the flip chart, a bound pad of large paper sheets mounted on a stand for sequential display during presentations, developed in the mid-20th century by Peter Kent to aid visual communication in meetings.[8] Flip-flops, meanwhile, designate simple backless sandals held to the foot by a thong between the toes, with modern rubber versions emerging in the United States post-World War II from repurposed tire rubber mimicking Japanese zori sandals introduced by soldiers.[9] These everyday items trace roots to ancient thong footwear but gained widespread casual use for beachwear and leisure after 1945.[10]Mathematics and statistics
Transformations and geometry
In Euclidean geometry, a flip, or reflection, is an isometry that maps each point of a figure to its mirror image across a specified line in the plane or plane in space, such that the line serves as the perpendicular bisector of the segment joining any point to its image.[11] This transformation preserves distances between points, as it belongs to the group of Euclidean motions, but it reverses the orientation of the figure, distinguishing it from direct isometries like rotations and translations that preserve handedness.[12] Formally, for a reflection over a line L, the image P' of a point P satisfies that the foot of the perpendicular from P to L is the midpoint of PP', ensuring collinearity and equal distance on opposite sides.[11] Reflections are involutions, meaning that applying the transformation twice yields the identity map, as the composition of two identical reflections over the same axis returns every point to itself; thus, each reflection has order 2 in the relevant symmetry group.[13] In the context of regular polygons, the flips (reflections) together with rotations generate the dihedral group D_n of order $2n, where n is the number of sides, comprising n rotations and n reflections, each reflection fixing one axis of symmetry through a vertex and midpoint or two midpoints.[14] These groups capture the full symmetry set of the polygon under rigid motions, with reflections providing the improper transformations that invert chirality.[15] The rigorous treatment of flips as part of transformation groups emerged in the 19th century, building on earlier intuitive uses in congruence proofs, with Felix Klein's Erlangen program of 1872 classifying geometries by their invariant transformation groups, including reflections as generators of Euclidean and other geometries.[16] This framework distinguished reflections from rotations by their orientation-reversing property, formalized through determinants of the associated linear maps (equal to -1 for reflections), enabling axiomatic developments in synthetic and analytic geometry.[13]Probability and statistics applications
The flip of a fair coin constitutes a Bernoulli trial, a random experiment with two outcomes—heads or tails—each occurring with probability p = 0.5.[17] In this model, each trial is independent, with the outcome determined solely by physical randomness absent any causal dependencies from prior flips.[18] For a sequence of n independent coin flips, the number of heads follows a binomial distribution \text{Bin}(n, 0.5), characterized by expected value \mu = np = n/2 and variance \sigma^2 = np(1-p) = n/4./05:_Probability/5.07:_Binomial_Distribution) This distribution underpins the law of large numbers, where the proportion of heads converges to 0.5 as n increases, verifiable through repeated empirical trials yielding relative frequencies approaching the theoretical probability.[19] Empirical studies reveal minor deviations in physical coin tosses; analysis of hand-flipped coins shows a dynamical bias where the outcome matches the starting face approximately 51% of the time, attributable to precession and wobble during flight rather than manufacturing defects or supernatural influences.[20] This bias diminishes with gentler tosses or mechanical flipping but remains negligible for large-scale statistical applications, where the fair-coin approximation suffices without altering convergence properties.[21] Coin flip models illustrate the gambler's fallacy, the erroneous belief that past outcomes—such as a streak of heads—influence future independent probabilities, leading to predictions of compensatory tails despite each flip retaining p = 0.5.[22] Causal independence ensures no "memory" in the process, debunking such intuitions through direct computation: the probability of heads remains unchanged post-sequence, as verified by binomial probabilities.[23] In Monte Carlo simulations, sequences of simulated coin flips approximate integrals or probabilities by averaging outcomes over many trials; for instance, estimating \pi via random points in a square enclosing a quarter-circle leverages binary decisions akin to flips for boundary checks.[24] Hypothesis testing employs flip data to assess coin fairness, computing p-values under the null of p = 0.5 via binomial tail probabilities, rejecting if observed deviations exceed critical thresholds derived from variance n/4./05:_Probability/5.07:_Binomial_Distribution)Science and technology
Electronics and computing concepts
A flip-flop is an electronic circuit with two stable states, functioning as a bistable multivibrator to store a single binary digit (bit) of information.[25] It serves as the core building block for sequential logic in digital systems, enabling state retention between clock pulses unlike combinational logic, which produces outputs solely from current inputs.[25] In central processing units (CPUs), arrays of flip-flops form registers that hold operands, addresses, and instruction states, synchronizing operations via clock signals to ensure predictable timing in pipelines and control units.[26] The first electronic flip-flop, the Eccles-Jordan trigger circuit, was patented in 1918 by British physicists William Eccles and F.W. Jordan, using vacuum tubes with positive feedback to achieve bistability.[27] This design laid the groundwork for modern implementations in transistors and integrated circuits, evolving through the mid-20th century with refinements for reliability and speed in computing hardware.[28] Common types include the SR (Set-Reset), JK, D (Data), and T (Toggle) flip-flops, each defined by input combinations and clocked behavior. The SR flip-flop uses Set (S) and Reset (R) inputs to toggle states, with a truth table as follows:| S | R | Q (next) |
|---|---|---|
| 0 | 0 | Q (prev) |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | Invalid |
| J | K | Q (next) |
|---|---|---|
| 0 | 0 | Q (prev) |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | ~Q (prev) |