power laws
Mathematical scaling patterns
Power laws are mathematical relationships where one quantity varies as a power of another: if you double the input, the output changes by a fixed multiple rather than a fixed amount.
They describe phenomena where small occurrences are common and large ones rare but not impossible—earthquake magnitudes, city populations, word frequencies, wealth distribution.
Income follows a power law: many earn little, few earn enormously.
The phrase often signals that extremes matter more than averages suggest.
Allocation across recipients
- exponentSuperscript showing power
- slopeAngled terrain or steepness
- heavy-tailedProne to extreme outliers
- alphaFirst Greek letter
scaling · frequency · rank · outliers · probability · curve fitting · regression · skewness
Economic inequality measure
- income distributionHow earnings are shared
- winner-take-allOnly champion receives reward
- concentrationSustained single-minded attention
- stratificationDivision into distinct levels
top-heavy · disparity · oligarchy · plutocracy · elites · long tail · dominance · market share
Sudden ground movement
- Richter scaleEarthquake strength measurement system
- avalanchesMassive snow collapses
- forest firesUncontrolled woodland blazes
- river networksConnected flowing water systems
fractals · magnitude · landslides · solar flares · extinction events
Central focal points
- nodesPoints of connection
- connectivityState of being linked
- clusteringForming concentrated groups
- viral spreadPathogen transmission between hosts
social networks · influence · centrality · network effects · exponential growth · cascades · superspreaders
distribution
Allocation across recipients
- exponentSuperscript showing power
- slopeAngled terrain or steepness
- heavy-tailedProne to extreme outliers
alpha · scaling · frequency · rank · outliers · probability · curve fitting · regression · skewness · empirical
wealth gap
Economic inequality measure
- income distributionHow earnings are shared
- winner-take-allOnly champion receives reward
- concentrationSustained single-minded attention
stratification · top-heavy · disparity · oligarchy · plutocracy · elites · long tail · dominance · market share · monopoly
earthquakes
Sudden ground movement
- Richter scaleEarthquake strength measurement system
- avalanchesMassive snow collapses
- forest firesUncontrolled woodland blazes
river networks · fractals · magnitude · landslides · solar flares · extinction events
hubs
Central focal points
- nodesPoints of connection
- connectivityState of being linked
- clusteringForming concentrated groups
viral spread · social networks · influence · centrality · network effects · exponential growth · cascades · superspreaders
power lawsequality
Same status for all
egalitarianism · regression to the mean · central tendency · diminishing returns · homogeneity
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