power law

Thân thiện

A scientist plots data points that follow a power law on a graph.

Definition

1. Noun:
   • A mathematical relationship where one quantity varies as a power of another: In psychophysics, a "power law" describes the principle that the perceived magnitude of a sensation (like brightness or loudness) increases in proportion to the stimulus intensity raised to a specific exponent.

Usage

• The term "power law" is used primarily in scientific contexts, especially psychophysics, to describe a specific type of non-linear relationship between a physical stimulus and its subjective perception.
• It is often cited as Stevens' power law, named after the psychologist S. S. Stevens who formulated it.

Examples

• Noun:
  • The perception of loudness follows a power law, meaning a tenfold increase in sound energy does not produce a tenfold increase in perceived loudness.
  • Stevens' power law is a fundamental model in psychophysics for understanding sensory scaling.

Advanced Usage

• "To obey/follow a power law": Describes a system or relationship that adheres to this specific mathematical principle.
  • Many natural phenomena, such as the distribution of earthquake magnitudes, are said to follow a power law.
• "Power-law relationship": A phrase used to emphasize the nature of the connection between variables.
  • Researchers identified a power-law relationship between city size and economic output.

Variants and Related Words

• Power-law distribution (n): A statistical distribution that follows a power law, often used in network science and complexity theory.
  • The frequency of word usage in a language often exhibits a power-law distribution.
• Power-law exponent (n): The specific numerical exponent in the power law equation that characterizes the rate of change.
  • The power-law exponent for brightness perception is less than one, indicating compression.

Synonyms

• Stevens' law: A direct synonym in the context of psychophysics.
• Psychophysical power function: A more descriptive technical synonym.

Related Phrases

• Scale invariance: A property often associated with power-law distributions, where the pattern looks the same at different scales.
• Log-log linearity: A characteristic of power laws; when plotted on logarithmic scales, the relationship appears as a straight line.

Học thuật

Noun

1. (psychophysics) the concept that the magnitude of a subjective sensation increases proportional to a power of the stimulus intensity

Từ đồng nghĩa

• Stevens' law
• Stevens' power law