Notes

Many of the things that scientists measure have a typical size or “scale”—a typical value around which individual measurements are centred.

e.g.: heights; weights; speeds of car on the Internet.

the ratio to the highest and lowest value is not very large (compared to what we'll be seeing next)

But not all things we measure are peaked around a typical value. Some vary over an enormous dynamic range, sometimes many orders of magnitude. A classic example

of this type of behavior is the sizes of towns and cities.

Other examples: In addition to city populations, the sizes of earthquakes, moon craters, solar flares, computer files and wars, the frequency of use of words in any human language, the frequency of occurrence of personal names in most cultures, the numbers of papers scientists write, the number of citations received by papers, the number of hits on web pages, the sales of books, music recordings and almost every other branded commodity, the numbers of species in biological taxa, people’s annual incomes and a host of other variables all follow power-law distributions.