[Fis] definition(s) of order/disorder ?

> Hence, the Bayesian word on order/disorder is that the distinction
always

remains relative to the chosen reference.

Dear Bob and colleagues,

>From an information-theoretical perspective every measurement is always
relative to the maximum information content of the system of reference.
When the system of reference is specified, the measurement can be very
precise and the hypothesis can be tested.

For example, if one assumes that a graphical representation contains a
symmetrical order, one can specify the graphical representation, for
example, in terms of its pixels. The maximum entropy is then equal to
the log of the number of pixels. One can then hypothesize that in the
case of perfect symmetry specific pixels would be precisely similar to
their symmetrical counterparts and test this hypothesis. The measurement
will enable us to specify, for example, how far the representation is
removed from symmetry in terms of bits of information.

Another hypothesis can be that the representation is containing
clusters. Information theory enables us to specify a cluster algorithm
that is exact, while all the multi-variate cluster analyses have to make
assumptions about the similarity criteria and in the clustering
algorithms. Information theory, however, works with a non-parametric
measure. I proved the algorithm for precise clustering in
<http://www.leydesdorff.net/jasist04> Similarity Measures, Author
Cocitation Analysis, and Information Theory, Journal of the American
Society for Information Science and Technology (JASIST), forthcoming; <
<http://www.leydesdorff.net/jasist04/cosine.pdf> pdf-version> . The
paper also contains an example.

Thus, the information-theoretical approach enables us to analyze
structures in data and to test hypotheses about these structures. It can
be elaborated to test for order, symmetry, clusters, etc. by the
specification of algorithms when the systems of reference are clearly
specified. The difference between the assumptions and the structure in
the data can be specified in terms of bits of information.

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
 <mailto:loet@leydesdorff.net> loet@leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/

 
 <http://www.upublish.com/books/leydesdorff-sci.htm> The Challenge of
Scientometrics ; <http://www.upublish.com/books/leydesdorff.htm> The
Self-Organization of the Knowledge-Based Society
 
Received on Mon May 24 18:50:54 2004