RE: [Fis] consilience of limited observers

Are you not describing here a fractal structure of nested hierarchies, where
self-similarity characterizes dynamics at various size and time scales?
Perhaps the epistemological work of philosophers Grim, Mar and Denis is of
relevance here (e.g., THe Philosophical Computer, MIT Press, 1998). These
researchers at SUNY use fractal images to model knowledge structures of
formal math/logic systems on the computer.

Best,
Terry

>Dear Aleks,
>
>One can expect that each network contains a structure. The network is built
>up relationally, but once in place it has an architecture. This structure
>can be described parsimoneously using its main axes, for example, using
>factor or cluster analysis. Each of these axes enables us to take a
>perspective from which the structure can be described hierarchically. In
>other words, one can expect a variety of perspectives allowing for
>hierarchies.
>
>When the perspectives can again be communicated like in science (in terms
>of
>observational reports) a second-order network layer is shaped relationally.
>Then one expects another set of eigenvectors and perspectives in this
>next-order network. When the first-order and the second-order networks
>resonate a system of communications tends to be closed like in a paradigm.
>In some sciences, one can expect therefore more paradigms than in others.
>
>For example, in physics the first-order perspectives are considered to be
>"data" that is given to us (in a Revelation?). In economics, different
>perspectives can compete while one agrees on the second-order perspective,
>but the data is constructed. In sociology, both levels are constructed and
>one hence can expect more than two 'paradigms'.
>
>Thus, there is a non-linear dynamics in the "consilience" of the
>reflections
>along different axes.
>
>With kind regards,
>
>
>Loet
>
> > -----Original Message-----
> > From: Aleks Jakulin [mailto:jakulin@acm.org]
> > Sent: Monday, October 25, 2004 8:42 AM
> > To: 'Loet Leydesdorff'; 'fis-listas.unizar.es'
> > Subject: 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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Received on Mon Oct 25 19:33:03 2004