RE: [Fis] probability versus power laws

From: Viktoras Didziulis <[email protected]>
Date: Thu 08 Jul 2004 - 08:44:14 CEST

 
 Dear Loet, colleagues,

>Would one not expect that the systems disturb each other in their recursive
selections albeit perhaps at the margins?
v: there is also a law of the first number (a.k.a. Benford's law)
accompanying the power laws (Zipf's, Pareto, etc). One can observe it in
nature as the presence of 1 dominant species in communities in amounts much
higher comparing with the rest species found there, etc... May this relate
with what you call margins ? Being an impatient speculator :) I would
imagine them as not necessarily margins in space but more as
functional-interacting margins' or 'communication gateways' of those systems
 

>these disturbances are also recursive, this would again lead to powerlaws,
wouldn't it?
v: theoretically recursive, iterative and self-reference processes
(evolution, growth, learning, and maybe communication...) should lead to
many sorts of powerlaws, fractals, self-similarity. I guess...

>In biological systems one would therefore expect powerlaws to prevail. But
in social systems, innovations are possible that would change the shape
(exponent) of the powerlaw? What would be the expectation in these cases (e
g., discourses)?
v: however some properties of social systems such as size of cities and
business enterprises are known to perfectly obey zipf's law. Maybe
innovations are a natural part of those like mutations or genes drift in the
living part of the nature.

>I assume that at a higher level of aggregation one would again expect
powerlaws in the distributions. Would it be possible to specify when one
would expect powerlaws and when not? Most situations are neither completely
random nor completely determined in social systems.
v: being on the edge of chaos (i.e. neither completely random nor completely
determined) is probably a property of the most systems in nature and those
systems usually are the systems showing behavior 'compatible' with power
laws. Uniform (i.e. truly random) distributions - do not.

I would suggest one more interesting reading related to Zipf's law and
communication in general. Their results strongly suggest that Zipf's law is
required by symbolic systems and is not a meaningless feature (!..) thus
reminding the last discussion on "what is meaning" on the FIS list:
Ramon Ferrer i Cancho and Richard V. Sole, 2003. Least effort and the
origins of scaling in human language. PNAS, vol. 100, no. 3. pp: 788-791.
www.pnas.org/cgi/doi/10.1073/pnas.0335980100

And if you search www.nature.com articles for "zipf's" keyword the output
will contain ~10 articles from various fields of science including social
science and economics. Just an interesting stuff...

Best regards
Viktoras



-------Original Message-------
 
From: Loet Leydesdorff
Date: Tuesday, July 06, 2004 23:08:38
To: 'Viktoras Didziulis'; fis@listas.unizar.es
Subject: RE: [Fis] probability versus power laws
 
Dear Viktoras, Stan, and colleagues,
 
Would one not expect that the systems disturb each other in their recursive
selections albeit perhaps at the margins? If these disturbances are also
recursive, this would again lead to powerlaws, wouldn't it? In biological
systems one would therefore expect powerlaws to prevail. But in social
systems, innovations are possible that would change the shape (exponent) of
the powerlaw? What would be the expectation in these cases (e.g.,
discourses)?
 
I assume that at a higher level of aggregation one would again expect
powerlaws in the distributions. Would it be possible to specify when one
would expect powerlaws and when not? Most situations are neither completely
random nor completely determined in social systems.
 
With kind regards,
 
 
Loet



Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
[email protected] ; http://www.leydesdorff.net/

 
The Challenge of Scientometrics ; The Self-Organization of the
Knowledge-Based Society




From: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es] On
Behalf Of Viktoras Didziulis
Sent: Wednesday, July 07, 2004 7:55 AM
To: fis@listas.unizar.es
Subject: Re: [Fis] probability versus power laws


 Power-law frequency distributions are known to reveal self-similarity and
fractal geometry in the underlying structures (B. Mandelbrot, 1997. Fractals
and self-affinity). In other words they reveal hierachy of real-world
structures (systems) and their composition. So naturally they have to be
widely spread thus being a good proof for the theory of hierarchies too.
 
Truly random events (characterized by uniform distributions) can not be
plotted in this manner. What's left - 'not (so) random' events/systems with
their internal structure and rules of their emergence/growth and
functioning/communication. So 'all what is left' follows power laws just
because they are parts of a structure being composed of yet smaller
structures, etc... Thus everything with fractal-like structure in nature is
a system.
 
In practice data points rarely ideally fits the power law distribution (not
a big surprise) and those distributions for different kinds of systems have
different slopes. So if data points plotted as a power law distribute into
different clusters along the line of power law (axes are logarithmic), then
most likely they belong to different systems. Or if some places show
substantial gaps, this should mean that system is under-sampled and it's
structure not completely represented.
 
Just suggestions. I am looking for more articles on this topic for more
proof. Also going to test those assumptions some time in future :)
with my own data.
 
Best regards
Viktoras
 
 
 
-------Original Message-------
 
From: Stanley N. Salthe
Date: Sunday, July 04, 2004 12:26:06
To: fis@listas.unizar.es
Subject: Re: [Fis] probability versus power laws
 
So, given that one can find power laws EVERYWHERE in ALL KINDS of
data, material and linguistic (just as one can do statistics anywhere), how
do you construe it that the susceptibility of data to being plotted as a
power laws suggest systems? What would be a result of an Xi by i (rank)
plot have to look like in order to falsify your system hypothesis?
 
STAN
 
 
 
_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis
.



 

IMSTP.gif
Received on Wed Jul 7 22:40:04 2004

This archive was generated by hypermail 2.1.8 : Mon 07 Mar 2005 - 10:24:47 CET