power law
Definition
- 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.
Noun
-
(psychophysics) the concept that the magnitude of a subjective sensation increases proportional to a power of the stimulus intensity
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