Tuesday, December 02, 2008

Mathematical Distributions -or- Why Free Will Is Bunk


Zipf’s law is a testament to the order in our world, showing that the same patterns emerge in a wide variety of situations. The linguist George Kingsley Zipf first proposed the law in 1949, when he noticed that the distribution of words in a newspaper, book, or other literary article always followed the same pattern.

Zipf counted how many times each word appeared, and found that the probability of the occurrence of words starts high and tapers off. Specifically, the most frequent word occurs about twice as often as the second most frequent word, which occurs about twice as often as the fourth most frequent word, and so on. Mathematically, this means that the frequency of any word is inversely proportional to its rank. When the Zipf curve is plotted on a log-log scale, it appears as a straight line with a slope of -1.

Since Zipf’s discovery, researchers have found that the power law describes many other natural and human phenomena, including the distribution of cities ranked by their population, the distribution of corporate wealth, and Internet traffic characteristics.

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Yet throughout the 12 years, the distribution of packages, as ranked by their number of incoming links from other packages, has followed Zipf’s law, with a few very popular packages having much greater connectivity than most.

PhysOrg


Interesting. So without our free will intervening, the number and distribution of packages in Linux distros matches this mathematical pattern.


The Poisson Distribution is a discrete distribution which takes on the values X = 0, 1, 2, 3, ... . It is often used as a model for the number of events (such as the number of telephone calls at a business or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies, e.g., to model the number of prairie dogs found in a square mile of prairie.

CSUSB


Translation: when you map linear numbers to reality, you find they follow a "bell curve" like distribution. This underlies events in our worlds, our own abilities, and our own thoughts -- great ideas tend to fit this pattern as well.

Still think you're autonomous and isolated from reality, an island? You're not. Nor do you have "free will." You are one more piece of the universe acting according to its patterns, which you can't touch or feel, but over time, they manifest themselves.

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Subvert the dominant paradigm, don't be a solipsist.

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