power laws

[Charles H. Davis]

Historically interesting but mathematically imprecise.  I'll try to keep
this in ASCII for general consumption.

There is a major difference between exponential (y=ae**bx) and a true
power curve (y=ax**b where x>0).  Since 1926 everyone has assumed the
pattern has been exponential.

The former falls off gradually; the latter drops dramatically.
 =======================================================================
Charles H. Davis, Ph.D., Senior Fellow          | Professor Emeritus
School of Library and Information Science       |        GSLIS
Indiana University at Bloomington               | University of Illinois
(812) 331-1322  Fax: (812) 855-6166             |    Urbana-Champaign
http://memex.lib.indiana.edu/davisc/davisc.html |
 =======================================================================

On Mon, 17 Jan 2000, Rousseau Ronald wrote:

> Dear Colleagues,
>
> May I point out that 'Lotka's law' studied by information scientists since
> 1926 is a power law. So is 'Zipf's law'. As far as I see it, information
> scientists have studied power laws since 'always'.
>
> The novelty of Sylvan Katz' approach lies in the fact that he has found
> new applications for these ubiquitous - power law - regularities.
>
> Ronald Rousseau
> KHBO - Zeedijk 101
> B-8400  Oostende  Belgium
>
>
> On Sat, 15 Jan 2000, Charles H. Davis wrote:
>
> > Dear Dr. Katz:
> >
> > Your communication was most welcome.  I've been trying for some time to
> > call power curves to the attention of the information science community.
> >
> > When I spoke with late Derek Price at an ASIS meeting in Banff in 1979, he
> > told me that he had "...thrown out a number of 'outliers'."
> >
> > See:
> >
> > D.J. de S. Price, "A General Theory of Bibliometric and Other Cumulative
> > Advantage Processes," JASIS 27:292-306 (1976).
> >
> > As a fellow physical scientist, I knew this was standard operating
> > procedure, but it worried me as he used the plural, not the singular.  It
> > has since come to my attention that acknowledgments follow a power curve
> > rather than an "ordinary" exponential distribution.  I'm now suspicious
> > about citation analysis generally and believe you or someone else should
> > pursue this idea.
> >
> > See also:
> >
> > Davis, Charles H. and Blaise Cronin, "Acknowledgments and Intellectual
> > Indebtedness: A Bibliometric Conjecture," Journal of the American
> > Society for Information Science 44(10):590-592 (December 1993).
> >
> > All this has has implications for how scientists actually do their work:
> > They may be as guilty of appeal to authority as historians.  What an
> > appalling thought!
> >
> > Please keep up the good work and stay in touch.  Thanks to the Internet,
> > we can now do such things easily.  Like you, I welcome observations from
> > all our colleagues.
> >
> > It's a new age.
> >
> > Cordially,
> >
> > Charles Davis
> > ========================================================================
> > Charles H. Davis, Ph.D., Senior Fellow          | Professor Emeritus
> > School of Library and Information Science       |        GSLIS
> > Indiana University at Bloomington               | University of Illinois
> > (812) 331-1322  Fax: (812) 855-6166             |    Urbana-Champaign
> > http://memex.lib.indiana.edu/davisc/davisc.html |
> > ========================================================================