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Reply With QuoteSo, infrastructure evolves just as creatures do--through natural selection. It also follows logic that we'd converge methods, as well (noting the lung=plumbing example).
Relevant to my interests.
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Thread: Zipf's Law
- 05-20-2009 06:27 PM #1let them eat cak Achievements:
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Zipf's Law
I tripped over this law on one of the NYTimes blogs and found it fascinating.
As stated in the blog,
Zipf originally applied the law to the frequency of words in a text, but it applies to a wide variety of data sets with no good explanation.The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows.If you have a sense of caring for others, you will manifest a kind of inner strength in spite of your own difficulties and problems. With this strength, your own problems will seem less significant and bothersome to you. By going beyond your own problems and taking care of others, you gain inner strength, self-confidence, courage, and a greater sense of calm.Dalai Lama
- 05-20-2009 07:25 PM #2Burnt Achievements:
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- 05-20-2009 08:45 PM #3Distinct among snowflakes Achievements:
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That's pretty neat. I took the liberty of graphing this in Excel for we visual folks:
As you can see, the top 25 US cities adhere pretty closely to Zipf's Law, although the actual populations overshoot the predicted populations pretty consistently (albeit not by much). Apparently our largest city needs to be a little bit bigger in order to put it all back into proportion.
- 05-20-2009 09:28 PM #4let them eat cak Achievements:
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Nice work on the graph! Zipf's law seems to hold consistently for the top 4 or 5, after which it seems like there are tiers or clusters, with 2 or 3 cities at the same level. Of course, deciding where to draw the line on a metro area is fuzzy these days, too, rendering the population numbers iffy.
If you have a sense of caring for others, you will manifest a kind of inner strength in spite of your own difficulties and problems. With this strength, your own problems will seem less significant and bothersome to you. By going beyond your own problems and taking care of others, you gain inner strength, self-confidence, courage, and a greater sense of calm.Dalai Lama
- 05-21-2009 12:44 PM #5Drivel's Advocate
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I wonder if this has some connection to a sort of critical mass effect. Once a city is known as 'the largest', all of a sudden twice as many people want to live there sort of thing.
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- 05-21-2009 05:04 PM #6Fireworks and Hurricanes Achievements:
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Hah, interesting. Good article about it on Wikipedia:
http://en.wikipedia.org/wiki/Zipf%27s_law
Check out the log log graph for word frequencies.
Apparently it also applies to random strings of words so it could just be an artefact... cool though.
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- 05-30-2009 11:11 AM #7Member
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This only seems to hold true for America. Looking at the other 3 of the top 4 most populous nations:
China:
1. Shanghai - 18,580,000
2. Beijing - 12,133,000
3. Guangzhou - 10,045,800
4. Shenzhen - 8,464,300
5. Xianggang (Hong Kong) - 7,000,000
India:
1. Mumbai - 13,922,125
2. Delhi - 12,259,230
3. Bangalore - 5,310,318
4. Kolkata (Calcutta) - 5,080,519
5. Chennai - 4,590,267
Indonesia:
1. Jakarta - 10,810,400
2. Bandung - 2,884,300
3. Surabaya - 2,729,300
4. Medan - 2,059,300
5. Bekasi - 1,994,850Greater than 99.9% of the people in the world fail to see that PhilosopherStoned is ideally suited to be the totalitarian dictator of the world in perpetuity. If you are one of the ones that do, copy and paste this into your signature.
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