Zipf's Law is the mathematical principle found across disparate subjects ranging from language to galaxy formation. The law is named after George Zipf, who studied it but did not claim to discover the law.
Basically, the law states that for a population, the largest will be twice as much as the second in the group, and three times as much for the third, and so on. In English language, the most popular word (the) is found twice as often and the second most popular word (of), and three times as much as the third (and), and so on through the English vocabulary.
This works for all languages, even invented languages.
This law holds true for a vast variety of different subjects, such as city populations, galaxy formation, number of television show viewers, corporations, solar flare intensity, diameter of moon craters, ingredients in recipes, last names, web traffic, and many more.
Why does this mathematical law hold across so many different things? The answer is: nobody knows. This is the strangeness of Zipf's Law. There aren't even any good theories to explain this strangeness. It's a pattern in the universe that will have to for now remain a mystery.
I do have a theory though, or more appropriately a hypothesis. I can't call it a theory, as I don't have any way to test it, and I don't make predictions. This is the theory: Nature is made up of morphic fields that organize structure and behavior of systems (for more on morphic fields, read Rupert Sheldrake's "A New Science of Life") and these fields are arranged according to mathematical laws. Nature is conservative, so the same mathematical laws are used multiple times and in multiple ways. This can also be thought of as archetypes, or forms. Nature conserves forms, as can be seen in "convergence" in evolution.
Convergence is the conservations of forms in different species, even over vast periods of time. For instance, the feline saber toothed cat, and it's older look alike, the marsupial saber toothed cat. Convergence is rife in marsupials and placentals. Consider, for instance, marsupial moles and dogs (now extinct). The marsupial dog's skull is nearly indistinguishable from a real dog's skull.
If there is convergence in biology, can there not be convergence in mathematical laws? Obviously, there can be. Zipf's Law shows this, and shows cosmos is more mysterious than we think.
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