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Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition
Wave_function_collapse
Family of algorithms used in procedural generation
Model synthesis (also wave function collapse or 'wfc') is a family of constraint-solving algorithms commonly used in procedural generation, especially
Model_synthesis
Interpretation of quantum mechanics
systems consisting of many particles, the collapse becomes stronger than the quantum dynamics. Then their wave function is always well-localized in space, so
Objective-collapse_theory
Mathematical description of quantum state
wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function
Wave_function
Interpretation of quantum mechanics
universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements
Many-worlds_interpretation
Non-mathematical introduction
certain value, and that this value is related to the Planck constant. Wave function collapse means that a measurement has forced or converted a quantum (probabilistic
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Area of physical and philosophical debate
the collapse of the wave function as resulting from a time-symmetric transaction between a possibility wave from the source to the receiver (the wave function)
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Nonlinear modification of the Schrödinger equation
large. Later on it was proposed as a model to explain the quantum wave function collapse by Lajos Diósi and Roger Penrose, from whom the name "Schrödinger–Newton
Schrödinger–Newton_equation
Interpretation of quantum mechanics
magnitude of the particle's wave function at that point. The concept of wave function collapse postulates that the wave function of a system can change suddenly
Copenhagen_interpretation
Theoretical problem in quantum physics
separates the wave packets in configuration space, which is where apparent wave function collapse comes from, even though there is no actual collapse. A fourth
Measurement_problem
Mathematical entity to describe the probability of each possible measurement on a system
Quantum harmonic oscillator Quantum logic gate Stationary state Wave function collapse W state Bures metric To avoid misunderstandings: Here we mean that
Quantum_state
Possible solution to the measurement problem
introduced as a possible solution to the measurement problem, where the wave function collapse is related to gravity. The model was first suggested by Lajos Diósi
Diósi–Penrose_model
Objective collapse theory in quantum mechanics
stochastic wave packet reduction postulate. The orthodox interpretation, or Copenhagen interpretation of quantum mechanics, posits a wave function collapse every
Ghirardi–Rimini–Weber_theory
Force resulting from the quantisation of a field
Vibrations in this field propagate and are governed by the appropriate wave equation for the particular field in question. The second quantization of
Casimir_effect
Interpretation of quantum mechanics
argued that the mathematics of quantum mechanics allows the collapse of the wave function to be placed at any position in the causal chain from the measurement
Consciousness_causes_collapse
Description of a quantum-mechanical system
Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a
Schrödinger_equation
Physics phenomenon
a particle's properties results in an apparent and irreversible wave function collapse of that particle and changes the original quantum state. With entangled
Quantum_entanglement
Fact that observing a situation changes it
out as a misconception rooted in a poor understanding of the quantum wave function ψ and the quantum measurement process. To "observe a particle" means
Observer_effect_(physics)
Class of theories in quantum mechanics
Hossenfelder, Sabine (2022-08-19). "Toy model for local and deterministic wave-function collapse". Physical Review A. 106 (2) 022212. arXiv:2010.01327. Bibcode:2022PhRvA
Superdeterminism
Principle of quantum mechanics
quantum superposition and every position wave function can be represented as a superposition of momentum wave functions and vice versa. These superpositions
Quantum_superposition
Topics referred to by the same term
the collapse of Soviet federalism State collapse Wave function collapse, in physics In medicine, collapse can refer to various forms of transient loss
Collapse
Mathematical tool in quantum physics
cannot explain wave function collapse, as all classical alternatives are still present in the mixed state, and wave function collapse selects only one
Density_matrix
Description of physical properties at the atomic and subatomic scale
which includes elements such as the "superposition of states" and "wave function collapse", give rise to the reality we perceive? More unsolved problems in
Quantum_mechanics
Fringe hypothesis
something to do with the workings of the mind. He proposed that the wave function collapses due to its interaction with consciousness. Freeman Dyson argued
Quantum_mind
Hypothetical interface between quantum events and a classical observer
mechanics, which requires a wave function collapse. Interpretations of quantum mechanics that do not recognise wave function collapse (such as De Broglie–Bohm
Heisenberg_cut
Loss of quantum coherence
possibility of the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse. It only provides a
Quantum_decoherence
German physicist (1901–1976)
cosmic rays, and subatomic particles. He introduced the concept of a wave function collapse. He was also instrumental in planning the first West German nuclear
Werner_Heisenberg
Thought experiment in quantum mechanics
problem: What constitutes a "measurement" that apparently causes the wave function to collapse into a definite state? More unsolved problems in physics Schrödinger
Schrödinger's_cat
2017 novel by Neal Stephenson and Nicole Galland
former MIT physicist who once worked on a device that could prevent wave function collapse. The device is somewhat like the box in the Schrödinger's cat experiment
The_Rise_and_Fall_of_D.O.D.O.
Quantum mechanical theory of spontaneous collapse
known as collapse) models is the CSL model. Building on the Ghirardi-Rimini-Weber model, the CSL model describes the collapse of the wave function as occurring
Continuous spontaneous localization model
Continuous_spontaneous_localization_model
Theory of a quantum origin of consciousness
computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process. In quantum mechanics
Orchestrated objective reduction
Orchestrated_objective_reduction
Problem in physics and quantum mechanics
system can be extracted from its wave function. Solving Schrödinger's equation allows you to find the wave function associated with a system, and therefore
Many-body_problem
Relativistic wave equation in quantum mechanics
In particle physics, the Klein–Gordon equation is a relativistic wave equation for spinless particles. It was discovered 1926 as the relativistic generalization
Klein–Gordon_equation
Interpretation of quantum mechanics
type of objective collapse theory. For these theories, the wavefunction is a physical wave, which experiences wave function collapse as a physical process
Penrose_interpretation
Interdisciplinary theory behind quantum computing
particle pairs, as the principles of the no-cloning theorem and wave function collapse ensure the secure exchange of the random keys. The development of
Quantum_information_science
Unintuitive aspects of quantum mechanics
Schrödinger's cat; the uncertainty principle; wave–particle duality; the probabilistic nature of wave function collapse, decried by Einstein, saying, "God does
Quantum_weirdness
Quantum mechanical phenomenon
the wave nature of matter and quantum indeterminacy. The quantum wave function describes the states of a particle or other physical system and wave equations
Quantum_tunnelling
Phenomenon resulting from the superposition of two waves
coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have
Wave_interference
Cryptography based on quantum mechanical phenomena
read the encoded data, the quantum state will be changed due to wave function collapse (no-cloning theorem). This could be used to detect eavesdropping
Quantum_cryptography
Popular science book by physicist Nick Herbert
causes collapse". First proposed by Eugene Wigner, this interpretation grants special status to conscious minds as the location of wave function collapse, in
Quantum_Reality
Calculation rule in quantum mechanics
rule states that an observable, measured in a system with normalized wave function | ψ ⟩ {\displaystyle |\psi \rangle } (see Bra–ket notation), corresponds
Born_rule
Quantum computing technique
{\displaystyle {\frac {1}{2}}} . What makes this undesirable is that wave-function collapse occurs before the program terminates, and thus may not yield the
Uncomputation
Claim that human mathematicians are not describable as formal proof systems
computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process. In quantum mechanics
Penrose–Lucas_argument
Electronic musician
Romantix (1998) We are DMX (1999) The Collapse of the Wave Function LP (2004) Many Worlds (The Collapse Of The Wave Function Volume 4) (2005) The Transactional
DMX_Krew
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
time evolution (e.g. ionization rates of atoms), and enhanced stationary wave intensities in regions of space where classical dynamics exhibits only unstable
Quantum_chaos
American scientist (1930–1982)
many-worlds interpretation (MWI). Everett's theory dropped the wave function collapse postulate of quantum measurement theory, incorporating the observer
Hugh_Everett_III
Device to determine relative phase shift
reflection and transmission of a wave at a dielectric imply that there is a phase change for a reflection, when a wave propagating in a lower-refractive
Mach–Zehnder_interferometer
Physics experiment
by the wave-function. So while a single particle will travel through one particular slit in the double-slit experiment, the so-called "pilot wave" that
Double-slit_experiment
View that mind is a ubiquitous feature of reality
does not take observation as central to the wave-function collapse, because it denies that the collapse happens. On the many-worlds interpretation, just
Panpsychism
French author
quantum mechanics, with no need for extra logical constructs such as wave function collapse." "We will never", Omnès believed, "find a common sense interpretation
Roland_Omnès
Physical quantity
average for sufficiently large numbers of collapses. Conservation of energy does apply during wave function collapse in H. Everett's many-worlds interpretation
Energy
Experiment verifying the wave-particle duality of matter
the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and also the wave mechanics approach of the Schrödinger equation. It was
Davisson–Germer_experiment
Interpretation of quantum mechanics
interpretation of quantum mechanics that postulates that, in addition to the wave function, a particle possesses a definite position at all times, even when unobserved
De_Broglie–Bohm_theory
Elementary particles with a spin of 1/2
{\frac {1}{2}}\hbar } . Note that these values for angular momentum are functions only of the reduced Planck constant (the angular momentum of any photon)
Spin_1/2
Formula for spectral line wavelengths in alkali metals
Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted
Rydberg_formula
Concept in Quantum mechanics
wave function collapse. The effect has been shown to be real. Ballentine later wrote papers claiming that it could be explained without wave function
Ensemble_interpretation
Thought experiment in theoretical quantum physics
splits into two parallel parts. According to objective-collapse theories, wave-function collapse occurs when a superposed system reaches a certain objective
Wigner's_friend
Physics experiment
polarizers can also be accounted for by considering the light to be a classical wave. However this experiment uses entangled photons, which are not compatible
Quantum_eraser_experiment
Relativistic quantum mechanical wave equation
the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four
Dirac_equation
Hypothetical group of multiple universes
experimentally unsupported processes and ad hoc postulates: finite space, wave function collapse and ontological asymmetry. Our judgment therefore comes down to
Multiverse
American alternative medicine advocate (born 1946)
to exhibit inherently quantum properties like interference and wave function collapse. Most literature on quantum healing is almost entirely theosophical
Deepak_Chopra
Converting classical mechanics to quantum mechanics
to be confused with a single particle system, since a single quantum wave function describes the state of a single quantum system, which may have arbitrarily
First_quantization
American physicist
theory, is given in his 2024 monograph Introduction to Dynamical Wave Function Collapse. This book presents CSL as two equations, a modified linear Schrodinger
Philip_Pearle
Interdisciplinary study of quantum physics and sociology
example is the idea of wave function collapse. In standard interpretations of quantum physics, a particle is described by a wave function, and attributes such
Quantum_social_science
Iconic quantum mechanics problem
quantum mechanics theory: how can the prediction of spherically symmetric wave function result in linear tracks seen in a cloud chamber. The problem was first
Mott_problem
Process in quantum mechanics
the 'einselection' account can really explain the phenomenon of wave function collapse remains unsettled. Zurek has defined einselection as follows: "Decoherence
Einselection
Theorem in quantum mechanics
exactly follow the classical trajectories. For general systems, if the wave function is highly concentrated around a point x 0 {\displaystyle x_{0}} , then
Ehrenfest_theorem
Interpretation of quantum mechanics
the wave function of the standard quantum formalism, and its complex conjugate, to be retarded (forward in time) and advanced (backward in time) waves that
Transactional_interpretation
Thought experiment in quantum mechanics
illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The statement is that a particle
Renninger negative-result experiment
Renninger_negative-result_experiment
Quantum mechanics principle
would change nothing and the total wave function would be unchanged. However, the only way a total wave function can both change sign (which is required
Pauli_exclusion_principle
Quantum states of two qubits
will "collapse" it into one of its basis states with a given probability. Because of the entanglement, measurement of one qubit will "collapse" the other
Bell_state
Use of the second law of thermodynamics to distinguish past from future
day-to-day experience of the arrow of time. A notable exception is the wave function collapse in quantum mechanics, an irreversible process which is considered
Entropy_as_an_arrow_of_time
Formulation of quantum mechanics
Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman
Heisenberg_picture
Science concerned with physical bodies subjected to forces or displacements
particles themselves are fields, as described theoretically by the wave function. The following are described as forming classical mechanics: Newtonian
Mechanics
Indian theoretical physicist (1894–1974)
left), he started to realize just how radical it was, and he compared it to wave/particle duality, saying that some particles didn't behave exactly like particles
Satyendra_Nath_Bose
Quantum mechanical waves describing matter
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical
Matter_wave
Lowest possible energy of a quantum system or field
the system as a harmonic oscillator, or wave function, that fluctuates between various energy states (see wave-particle duality). All quantum mechanical
Zero-point_energy
Special low-energy state in quantum mechanics
well-defined quantum event (wave function) at some earlier location in classical space and time. The originating wave function relates the two entities in
Singlet_state
Interpretation of quantum mechanics
macroscopic world is assumed to be intrinsically classical in nature, and wave function collapse occurs when a quantum system interacts with macroscopic apparatus
Relational_quantum_mechanics
American comic book series
of time travel would predetermine the entire future timeline by wave function collapse. However, Snow personally turns on the time machine, and his intent
Planetary_(comics)
Relativistic interaction in quantum physics
that the electrostatic potential is spherically symmetric, so is only a function of radius. This approximation is exact for hydrogen and hydrogen-like systems
Spin–orbit_interaction
Different states of quantum systems
such as an electron in an atom, the wave functions that have well defined energies have the form of a standing wave. States having well-defined energies
Energy_level
Quantum mechanical model
representing this eigenvalue problem in the coordinate basis, for the wave function ⟨ x | ψ ⟩ = ψ ( x ) {\displaystyle \langle x|\psi \rangle =\psi (x)}
Quantum_harmonic_oscillator
Concept in quantum mechanics
Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave
Wave–particle_duality
Background energy existing in space
changes in the strength of, such a field to propagate as per the appropriate wave equation for the particular field in question. The second quantization of
Vacuum_energy
Hydrodynamic formulation of the Schrödinger equations
the flow velocity, defined in terms of the phase of the Schrödinger wave function ψ ( x , t ) {\displaystyle \psi (\mathbf {x} ,t)} below, ρ m ( x , t
Madelung_equations
Interpretation of quantum mechanics
of a quantum state changing when a measurement occurs—the "collapse of the wave function"—is simply the agent updating her beliefs in response to a new
QBism
Extension of the Bohr model
current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics, which Erwin Schrödinger developed in 1926. However, this is not
Bohr–Sommerfeld_model
Predecessor to modern quantum mechanics (1900–1925)
a more mathematical form by Einstein, who noted that the phase function for the waves, θ ( J , x ) {\displaystyle \theta (J,x)} , in a mechanical system
Old_quantum_theory
Quantum physics thought experiment
detectors, and that under the other configuration two copies of the wave function, traveling over different paths, arrive at both detectors, are out of
Wheeler's delayed-choice experiment
Wheeler's_delayed-choice_experiment
Type of quantum mechanics theory
to clearly enunciate the probabilistic interpretation of the quantum wave function, which had been introduced by Erwin Schrödinger earlier in the year
Hidden-variable_theory
Sum or aggregate of all that is real or existent
precipitates collapse of the wave function, independent of any realist interpretation. Commonly known as "consciousness causes collapse", this controversial
Reality
Formulation of quantum mechanics
between the initial and the final point also contribute. In terms of the wave function in the position representation, the path integral formula reads as follows:
Path_integral_formulation
.} - wave function of the state of the system Ψ {\displaystyle \Psi } - total wave function of a system ψ {\displaystyle \psi } - wave function of a system
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Set of mathematical concepts in quantum gravity
using transition functions. Because the six-dimensional manifold cannot be covered with a single coordinate system, transition functions are grouped together
Quantum_geometry
Notation for quantum states
state U|ψ⟩, the same U for every possible |ψ⟩. Wave function normalization is scaling a wave function so that its norm is 1. Since virtually every calculation
Bra–ket_notation
Interpretation of quantum mechanics
The main difference lies in the meaning of the reduction rule for 'wave packet collapse'. In the new approach, the rule is valid but no specific effect on
Consistent_histories
Interpretation of quantum mechanics
Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman
Local_hidden-variable_theory
Active acquisition of information from a primary source
state—not in a mixture. The act of measurement appears to cause the wave function collapse, transitioning the system from a superposition to a single, determinate
Observation
Notation for conserved quantities in physics and chemistry
framework for predicting the properties of atoms. When Schrödinger published his wave equation and calculated the energy levels of hydrogen, these two principles
Quantum_number
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
Boy/Male
English
Alert.
Female
Irish
Variant spelling of Irish Maeve, MAVE means "intoxicating."Â
Surname or Lastname
English
English : from the Middle English personal name Wade, Old English Wada, from wadan ‘to go’. (Wada was the name of a legendary sea-giant.)English : topographic name for someone who lived near a ford, Old English (ge)wæd (of cognate origin to 1), or a habitational name from a place named with this word, as for example Wade in Suffolk.Dutch and North German : occupational name or nickname from Middle Dutch, Middle Low German wade ‘garment’, ‘large net’.Jonathan Wade emigrated from Norfolk, England, to Medford, MA, in 1632. Benjamin Franklin Wade (1800–1878), born near Springfield, MA, was a prominent U.S. senator from OH during the Civil War.
Male
English
English short form of Hebrew David, DAVE means "beloved."
Surname or Lastname
English
English : from a Germanic personal name Walo, either a byname meaning ‘foreigner’ (see Wallace), or else a short form of the various compound names with this first element.English : nickname for a well-liked person, from Middle English wale ‘good’, ‘excellent’ (originally meaning ‘choice’).English : topographic name for someone who lived near an embankment, Middle English wale (Old English walu).
Boy/Male
Anglo Saxon English
Wise.
Boy/Male
Hindu
Variant of David beloved
Boy/Male
Indian
Friction
Surname or Lastname
English
English : occupational name for a servant, from Middle English knave ‘boy’, ‘youth’, ‘servant’.English : possibly a metonymic occupational name for a maker of wheel-hubs, Middle English nave (from Old English nafa, nafu).German (also Näve) : variant of Neff (see Neve).Dutch (de Nave) : variant of Naef 1.In some cases possibly Portuguese : topographic name from nave ‘plain’ (a variant of nava), or a habitational name from a place named with this word. Compare Nava.
Boy/Male
Anglo Saxon American English Scandinavian
Moving.
Girl/Female
Irish
Joy.
Surname or Lastname
English (of Norman origin) and northern French
English (of Norman origin) and northern French : nickname for a bald man, from Anglo-Norman French cauf ‘bald’. Compare Chaffee.English : habitational name from a place in East Yorkshire called Cave, apparently from a river name derived from Old English cÄf ‘swift’.French : metonymic occupational name for someone employed in or in charge of the wine cellars of a great house, from Old French cave ‘cave’, ‘cellar’ (Latin cavea, a derivative of cavus ‘hollow’).French, possibly also English : topographic name for someone who lived in or near a cave, from the same word as in 3 in an older sense.
Boy/Male
Anglo, British, English, Jamaican
Wise; Watchful; Aware; Watchman; Careful
Girl/Female
Slavic
Stranger. Pet name formed from Varvara; the Russian form of Barbara.
Boy/Male
Hebrew American Scottish Welsh
Cherished; Beloved.
Male
English
 English topographical surname transferred to forename use, WADE means "lives near the river crossing." Middle English form of Anglo-Saxon Wada (the name of a sea giant), meaning "to go," in the sense of going forward, proceeding.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : topographic name for someone who lived by a dam or weir on a river (Old English wær, wer), or a habitational name from a place named with this word, such as Ware in Hertfordshire.English : nickname for a cautious person, from Middle English war(e) ‘wary’, ‘prudent’ (Old English (ge)wær).English : Robert Ware came to Dedham, MA, from England in or before 1642. Henry Ware (1764–1845), born in Sherborn, MA, was a Unitarian clergyman and theologian and father of the physician John Ware (b. 1795) and two clergymen, Henry (b. 1794) and William (b. 1797).
Boy/Male
Anglo, British, English
Alert; Watchman
Surname or Lastname
English
English : variant spelling of Way.
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
Boy/Male
Australian, Latin
Crowned with Laurel; From Laurentium; Laurentium was a City South of Rome Known for Its Numerous Laurel Trees
Girl/Female
Muslim
Happy for entire life
Male
Hawaiian
Hawaiian name NAHELE means "forest."
Boy/Male
Arabic, Muslim
Bright Star
Boy/Male
Hindu, Indian
Boundless; Guest; Mother of Gods
Boy/Male
British, English, Hebrew
Right-hand Son; Similar to Benedict
Boy/Male
Irish
Scandal.
Boy/Male
French
Born during Advent.
Surname or Lastname
French
French : from the personal name Valére, from Latin Valerius (see Valerio).English : topographic name for a dweller in a valley, from a noun derivative of Old French val ‘valley’ or possibly Middle English valeye.A Vallier, also recorded as Valliere and Vallieres, from the Saintonge region of France, is documented in Quebec City in 1667.
Girl/Female
Tamil
A garland of types of flowers
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
WAVE FUNCTION-COLLAPSE
a.
Pertaining to, or connected with, a function or duty; official.
a.
Exhibiting a wavelike form or outline; undulating; intended; wavy; as, waved edge.
n.
The things sold by auction or put up to auction.
v. t.
To sell by auction.
a.
Pertaining to the function of an organ or part, or to the functions in general.
n.
A wave.
imp. & p. p.
of Wave
v. i.
To play loosely; to move like a wave, one way and the other; to float; to flutter; to undulate.
v. t.
To give sanction to; to ratify; to confirm; to approve.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
v. t.
The act of uniting, or the state of being united; junction.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
v. t.
To move like a wave, or by floating; to waft.
n.
A wave.
n.
The act of anointing, smearing, or rubbing with an unguent, oil, or ointment, especially for medical purposes, or as a symbol of consecration; as, mercurial unction.
v. t.
See Waive.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
v. i.
To fluctuate; to waver; to be in an unsettled state; to vacillate.