Hi Folks,

Today I’m going to re-cap a most interesting mathematical property to model natural interaction between two or more living beings – The zipf property. It was introduced in the early 20th century where it kept un-noticed until it was used by famous mathematicians. The property was named after George Zipf (1949) who first popularized the empirical finding.

We have complex messy models, yet reality is startlingly neat and simple

– Paul Krugman (1996)

I’m a so-called believer that any complex model can be reduced to simple general phenomena what my grand-mother is capable enough to understand. Actually zipf property did pay the attention among many researches to have a unique way to see the architecture of a problem. It was occupied & argued by many researchers from physics, economics, linguistics, and geography for several decades.

Zipf was begun to popular when researches used it to model the the population in natural cities.  For an example if we tabulate all the cities of a country and rank them according to their size, e.g. by population, the first largest city is twice as big as the second largest, three times as big as the third largest, and so on. To put it another way, the size of a city is inversely proportional to its rank.

Actually this observation is valid for many interesting situations. Let’s look at some of them:

• “The” – most frequent word used in world wide web is followed by the terms “of”, “and”, “to” are following the zipf distribution.
• Ranks of number of people watching the same TV channel also does follow the zipf distribution.

In general, we can model any interaction between two living beings as a zipf distribution. Simply speaking, the word & the behavior which I’m used to interact with this blog readers do follow the zipf. This distribution model is very much important in statistical operations where you can not deal with average, mean kind of metrics any more. Implicitly, zipf does follow the power law.

In many researches, it’s obvious choice to have a user evaluation to see the effectiveness of the proposed model. But if you can align your model with zipf property, you will no longer required to have a cumbersome user evaluation. Keep up with GeekTube405 to explore the great power of zipf!