Zipf’s law and the distribution of cities

[El Presidente]

Doing some study on complexity  theory.  Came across Zipf's laws. I found it fascinating at least particularly as it pertains to cities 

 

 Zipf's law implies that, in a system of cities, the largest city is roughly twice the size of the second largest city, about three times the size of the third largest city, and so on. ... 

Largest cities in the USA

 

Here is a ranking of the 10 largest cities in the USA.

Rank	City	Population
1	New York, N.Y.	8,491,079
2	Los Angeles, Calif.	3,928,864
3	Chicago, Ill.	2,722,389
4	Houston, Tex.	2,239,558
5	Philadelphia, Pa.	1,560,297
6	Phoenix, Ariz.	1,537,058
7	San Antonio, Tex.	1,436,697
8	San Diego, Calif.	1,381,069
9	Dallas, Tex.	1,381,069
10	San Jose, Calif.	1,015,785

 

There are anomalies, but the theory holds up well across the globe.   Complexity theory is not as dry as I thought it would be 

 

 

[mprach024]

Good ol’ George Zipf, of course we all know him well.  ?

Boss you need me to send you some suggested books, movies, tv shows?  

[El Presidente]

2 minutes ago, mprach024 said:

Good ol’ George Zipf, of course we all know him well.  ?

Boss you need me to send you some suggested books, movies, tv shows?  

I am happy just to get the "gist " of it.  

[RedLantern]

How do you account for "city" vs metro area? For example, the distinction between NYC proper and other contiguous development is a legal distinction not a cultural or social one.

[Fuzz]

Well, it doesn't work here....

[Zaxeiler]

In a system of cigar producers, is the largest selling twice the volume of the second largest... ?

[El Hoze]

On 11/18/2020 at 10:03 PM, RedLantern said:

How do you account for "city" vs metro area? For example, the distinction between NYC proper and other contiguous development is a legal distinction not a cultural or social one.

I believe if you look at it as metro area to metro area the same math plays out. 

Lots of complexity references on the board lately, another post yesterday referenced Murray Gell-Mann who founded the Santa Fe Institute, a think tank focused on complex adaptive systems. Also today on google is a dedication to Benoit Mandelbrot.

I have my undergrad in applied math and statistics and reading Gell-Mann or Mandelbrot and I’m over my head pretty quickly. But super cool stuff.