The Colours of Infinity by Nigel Lesmoir-Gordon

Author:Nigel Lesmoir-Gordon [Lesmoir-Gordon, Nigel]
Language: eng
Format: epub
Tags: Technology & Engineering, Geometry, Science, General, Mathematical Physics, Mathematics, Physics, Engineering (General)
ISBN: 9781849964852
Publisher: Springer
Published: 2010-12-29T05:00:00+00:00

self-organIzaTIon, self-regulaTIon, and self-sImIlarITy on The fraCTal Web 101

There are multiple factors that can lead to the dif-

ferences in competition that we see. For commercial Zipf’s Law

wedding sites, one factor could be their local nature: The Web is not alone in exhibiting power laws.

many wedding-related retailers serve only a local area, Data gathered on the use of language, the

and those serving different areas usually do not compete.

population of cities, and the distribution of

wealth all show clear power-law behaviour. The

Another factor may be that people looking for wedding

frequency of words used in human language

services use methods other than the Web more often

deserves special mention: it follows the famous

(e.g. referrals from friends). Perhaps because people use Zipf’s Law, named after George Kingsley Zipf,

wedding providers rarely, they are less likely to create an early twentieth-century scientist who revolu-tionized our understanding of power laws, and

and share information among related sites on the Web.

helped to reveal their astonishing prevalence

Note that more difficulty competing with existing

throughout society and nature.

popular sites does not mean that substantially bet-Zipf’s Law states that the most common word

ter newcomers cannot become popular quickly. For

used in language is a constant factor (say, two

example, Google (a relative latecomer to the search

times) more common than the second most

common word, and the second most common

business) has captured a huge fraction of the Web is twice as common as the third, etc. Remark-search business largely by providing better service ably, for almost any sizeable source of words

and spreading through word of mouth.

you can think of – all New York Times articles, or all the works of Shakespeare, or all textbooks

on molecular biology, or the Bible – Zipf’s law

The Web is a Bow Tie

holds.

In 2000, a collaboration of scientists from AltaVista,

In 1955, Herbert Simon sought to unify the

observations of Zipf and others by formulating

IBM, and Compaq [Broder 2000] discovered a fas-a single common explanatory model for many

cinating property of the Web: somehow, all of the of the systems displaying power-law behaviour,

billions of pages and links have organized them-

including language, population, and wealth.

selves into an overall bow tie shape as pictured in Benoît Mandelbrot [1953,1959] proposed a

fascinating alternative explanation for Zipf’s

Figure 6.8. The centre of the bow tie is a core of Law as it relates to language. He showed that

strongly connected pages: every one of these pages the distribution can be understood as the end

can be reached from any other page within the core

result of centuries of adaptive maximization of

by clicking on a sequence of links (the sequence may

the information content of language.

need to traverse a number of intermediate pages, but

some path exists between the two core pages). The

left bow is connected to the core, but only through

the Web (the core, the left bow, the right bow, and

outgoing links. That is, there exist links from the the disconnected pages). To their surprise, all four left bow to the core, but not vice versa. Conversely,

components were roughly the same size.

the right bow is connected from the core only via A year later, some of the same scientists [Dill inbound links.

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