RE: [Fis] consilience of limited observers

In this post I discuss how hierarchies relate to networks and factor
analysis. There are hierarchical networks, and hierarchical factors.
Furthermore, if you don't want to see hierarchies, you will see certain
"patterns" that can be seen as resulting from hierarchies, such as hubs.

Loet wrote:
> "Data reduction" can be addressed with standard techniques
> like factor analysis. The assumption of a normative starting
> point may obscure the structure in the data. In the case of
> the sciences, the differentiation into specialties is robust.
> Professional associations and journals, for example, are
> firmly shielded against outsiders. General science journals
> (Nature, Science, New England Journal of Medicine) have
> specific communication functions across otherwise firmly
> delineated fields.

"Hierarchy" is our mental language for describing reality. Nothing *is*,
we're just observers. Particles are in our minds, not in reality. Waves are
in our minds, not in reality. Numbers are in our minds, not in reality.
Hierarchies are just one way of making sense in the flutter of photons
striking our eyes. We can judge them through how well they simplify our view
of reality. Of course, some of the detail is thrown away, but that's
inevitable. The question is whether hierarchies deserve to be in our
toolbox. Just as you cannot accomplish everything with hammers, you need
shovels, pickaxes, dynamite and other tools in addition to hierarchies. Of
course, we have to assume certain things to "be" if they are very useful,
but this just means that we don't question them that often.

Such tools are factor analysis, which can be combined with hierarchies into
hierarchical factor analysis, see A. Jensen's "The G Factor" (1998) -- the
`g factor' is justified precisely through hierarchical factor analysis).
Clustering is quite similar to factor analysis, but the factors are
discrete. Again, there is hierarchical clustering that I'm personally using
quite a lot.

Another tool is network analysis which you use yourself. Again, it can be
complemented with hierarchies - there is hierarchical network analysis,
where there are networks hidden inside nodes:

Erzsebet Ravasz and Albert-Laszlo Barabasi, "Hierarchical organization in
complex networks," cond-mat/0206130

M. Copelli, R. M. Zorzenon dos Santos and J. S. Sa Martins, "Emergence of
Hierarchy on a Network of Complementary Agents," cond-mat/0110350;

Roger Guimera, A. Arenas and A. Diaz-Guilera, "Communication and optimal
hierarchical networks," cond-mat/0103112;

(more pointers at
http://cscs.umich.edu/~crshalizi/notebooks/complex-networks.html )

Imagine that each paper is itself a network of ideas, and each idea is a
network of facts.

> In sum: there is not much hierarchy in the data.

If you look at a single level (connections between papers), you're
definitely not going to see the networks of ideas within the paper, the
networks of roles of different researchers, the networks of departments
within institutions, the networks of institutions within states, the
networks of collaborators within a field. Indeed, research authorities that
may seem to be on a different level will look like authoring hubs in this
flattened representation, and publishing authorities will again look as
citation hubs. This matter is very important in modern computer science:
Google works so well because of the PageRank algorithm, which is based on
discovering authoritative sources based on how many web "citations" they
get. If your web page is cited by one of such authorities, it appears higher
up in the Google list of results.

Also, you mention clusters. The fact that there are clusters usually
indicates hierarchies to the top. Imagine a network of two warring armies:
most of the connections will be inside the army, not in between. In the
present political circumstances, take a look at connections between book
purchases http://weblog.infoworld.com/udell/gems/valdisBooks.jpg

Best regards,
                Aleks

--
mag. Aleks Jakulin
http://www.ailab.si/aleks/
Artificial Intelligence Laboratory, 
Faculty of Computer and Information Science, University of Ljubljana. 
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