- Paperback: 588 pages
- Publisher: Martino Fine Books (June 6, 2012)
- Language: English
- ISBN-10: 161427312X
- ISBN-13: 978-1614273127
- Product Dimensions: 6.7 x 1.2 x 9.6 inches
- Shipping Weight: 2.1 pounds (View shipping rates and policies)
- Average Customer Review: 4.1 out of 5 stars See all reviews (4 customer reviews)
- Amazon Best Sellers Rank: #1,192,552 in Books (See Top 100 in Books)
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Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology
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Top Customer Reviews
Zipf's main contribution was that (a) he was the first to hypothesize that there is a universal principle at play, and (b) he proposed a mathematical formula to describe it. Although his attempts to derive a comprehensive theory were incomplete (and some say misguided), his mathematical formula was pretty accurate.
Zipf's work had considerable influence on a young graduate student, named Benoit Mandelbrot, who went on to develop the field of fractals.
Zipf's law models the scaling (fractal) properties of many phenomena in human ecology, including natural language and music. Zipf's law is one of many related laws that describe scaling properties of phenomena studied in the physical, biological, and behavioral sciences. These include Pareto's law, Lotka's law, power laws, Benford's law, Bradford's law, Heaps' law, etc.
Informally, Zipf's law describes phenomena where certain types of events are quite frequent, whereas other events are rare. For example, in English, short words (e.g., "a", "the") are very frequent, whereas long words (e.g., "anthropomorphologically") are quite rare.
Surprisingly, if we compare a word’s frequency of occurrence to its statistical rank, we notice an inverse relationship. The most frequent word occurs 2 times as many as the 2nd most frequent word, 3 times as many as the 3rd most frequent word, and so on. To put it differently, if the most frequent word occurs 1000 times, the 2nd most frequent word will occur 500 times (1000 divided by 2), the 3rd most frequent word 333 times (1000 divided by 3), and so on. This applies to all regular books written in English and other languages. Some fluctuations occur, and those have been shown to relate to language (English vs. French, etc.), writing style, etc.
Also, the same type of analysis has been used to identify composer, style, and even pleasantness of musical pieces.
Zipf distributions have been discovered in a wide range of human and naturally occurring phenomena, including music, city sizes, incomes, subroutine calls, earthquake magnitudes, thickness of sediment depositions, clouds, trees, extinctions of species, traffic jams, and visits to websites. Moreover, it has been convincingly suggested that Zipf's law captures a balance that feels natural and even aesthetically pleasing to humans, for certain phenomena, such as music, urban structures, and landscapes.
Zip's law is captured by the formula:
P(f) ~ 1/f^n
where P(f) denotes the probability of a word (or event) of rank f, and n is close to 1. In physics, Zipf's law is a special case of a power law. When n is 1 (Zipf's ideal), the phenomenon is called 1/f or pink noise. When n is 0 it is called white noise. When n is 2 it is called 1/f^2 or brown noise.
Mandelbrot generalized Zipf's formula to account for all types of scaling phenomena in nature.
An influential book. At places, very inspiring. At other places, hard to read. A must for any student of fractals, power laws, and self-organized criticalities. The universe is regularly organized and harmoniously put together, if you know how to look at it. Some will say that Zipf pointed the way, with this book.
In short what Dr. Zipf proposes is that things will generally take the line of least resistance. What he has done is almost that eloquent, and almost as universal as he clearly believes.
Beginning with a simple argument
From the point of view of the speaker, a language of one word- a word that achieves everything the speaker needs is perfect.
From the point of view of the listener, a language where every word has its own unique meaning insures that the listener has no problems understanding; is perfect.
Professor Zipf then demonstrates that the dynamic created by these two extremes can be demonstrated as a mathematical statement and that the graph of this equation can be applied to topics as far apart as the allocation of column inches in a Newspaper and the allocation of money in an economic system.
In fact his equation, and more exactly the chart of its output are known as Zipf's law or the zeta distribution. By charting his predicted distribution as a natural log of the values on both the X and y axis, the reader is presented with a simple sloped line. The book will demonstrate dozens of examples wherein there is no objective reason why the data should distribute as The Law says, except that The Law seems to hold.
Most interesting is his argument that ALL Economic systems, and by extensions, all societies MUST distribute wealth according to this same slope or risk being unstable, as in subject to violent revolt The violence only serving to reinstate a distribution that will restore reinstate the predicted slope. Lots of people getting just enough to survive and layers of increasing wealth distributed to ever fewer people.
The math works out from the bottom as the chances of being in the bottom spot is twice that of being in the next one up which is twice that of being in the next one up until you reach the top who are pretty much always going to be on the top. He does allow for upward mobility, but anyone moving up has to mean someone else is moving down.
It is because of his politics and his insistent inflexibility that Zipf is not as influential as was his sel-confident belief he was by right. That is he believed he had created and proved the single most important driving, objective fact of the human condition. Adopt his point of view and all policy making, religious beliefs and trips to buy groceries are no more complex that whatever answer his math generates.
It is a fact that Zepf's law has applications. He has directly influenced, among other things things web design.
An unintentional aspect of this book has to do with the field of statistics. Although the entire power of his Law is based on the statistical relationships Professor Zipf uses as examples, he had very little ability to test his results. There is nothing here of confidence intervals, or controlling of variables while performing multiple regression. In this sense this book can serve as an example of how much harder it can be to prove a hypothesis without having the tools to properly test your results.
This was one of the hardest books I have read in many years. It is not a casual read. The lack of modern statistical techniques may render it near useless as a study in stats. My recommendation is that you should not confuse this with typical summer reads, but it is deserving of respect.