Re: [OPE-L] Absolutes in Marxian Theory?

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Mon Jan 02 2006 - 16:01:45 EST

I am attaching an explantory note that I recently
wrote on the difference between power law and 
Boltzmann Gibbs distributions.

The Wikepedia account accords with my understanding of it.

-----Original Message-----
From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Paul Zarembka
Sent: 01 January 2006 20:48
Subject: Re: [OPE-L] Absolutes in Marxian Theory?

I have experience that Wikipedia leaves a lot to desired in terms of
being a responsible source.  Maybe it's OK for this, maybe not. Paul Z.

RESEARCH IN POLITICAL ECONOMY,  Paul Zarembka, editor,  Elsevier Science

On Sun, 1 Jan 2006 glevy@PRATT.EDU wrote:

> Hi Paul Z,
> I'll let Ian answer your question more.  Here is part of the
> the free encyclopedia, entry for power law.  I guess the more precise
> way of stating Ian's claim is that income distribution follows a
> power law probability distribution (see last section below).
> In solidarity, Jerry
> ======================================
> A power law relationship between two scalar quantities x and y is any
> that the relationship can be written as
>       k
> y = ax
> where a (the constant of proportionality) and k (the exponent of the
> law) are constants.
> Power laws can be seen as a straight line on a log-log graph since,
> logs of both sides, the above equation is equal to
> log (y) = k log (x) + log (a)
> which has the same form as the equation for a line
> y = mx + c
> Because both the power law and the log-normal distribution are
> distributions, they can be notoriously easy to confuse without using
> robust statistical methods such as Bayesian model selection or
> hypothesis testing. One rule of thumb, however, is if the distribution
> straight on a log-log graph over 3 or more orders of magnitude.
> Power laws are observed in many fields, including physics, biology,
> geography, sociology, economics, linguistics, war and terrorism. Power
> laws are among the most frequent scaling laws that describe the scale
> invariance found in many natural phenomena.
> Examples of power law relationships:
>   a.. The Stefan-Boltzmann law
>   b.. The Gompertz Law of Mortality
>   c.. The Ramberg-Osgood stress-strain relationship
>   d.. The inverse-square law of Newtonian gravity
>   e.. Gamma correction relating light intensity with voltage
>   f.. Kleiber's law relating animal metabolism to size
>   g.. Behaviour near second-order phase transitions involving critical
> exponents
>   h.. Frequency of events or effects of varying size in self-organized
> critical systems, e.g. Gutenberg-Richter Law of earthquake magnitudes
> and Horton's laws describing river systems
>   i.. Proposed form of experience curve effects
>   j.. Scale-free networks, where the distribution of links is given by
> power law (in particular, the World Wide Web)
>   k.. The differential energy spectrum of cosmic-ray nuclei
> Examples of power law probability distributions:
>   a.. The Pareto distribution
>   b.. Zipf's law
>   c.. Weibull distribution
> These appear to fit such disparate phenomena as the popularity of
> websites, the wealth of individuals, the popularity of given names,
> the frequency of words in documents.

This archive was generated by hypermail 2.1.5 : Tue Jan 03 2006 - 00:00:01 EST