Some odd comments to the W W W: Complex System (Chaos Theory) an d A Mathematical Definition

Hi.

  I was reviewing the WebArch WD [1], and a few interesting points came in
mind.  Although the following ideas can be outside the scope of the
technical report, I feel the need to express this thoughts :-)

1) As a part of the Architecture of the WWW, it is useful to describe a
mathematical definition of it, based on the Set Theory.  As when you define
a deterministic automaton as a Set of components (states, transitions, final
states, etc.), the WWW system can have an alike definition.  For Example:
 The World Wide Web (WWW) is an information space, thus can be thought of a
mathematical set of:
- WWW = { R, U, P } where 
R is the universal set of resources, 
U refers to the universal set of URI's that identify each resource (and
sub-resource?) and 
P conforms to the universal set of digital representations of each resource
based upon computational constructions...

2) Also, because of its evolve nature, the WWW system can be though as a
Complex and Dynamical System based on the Chaos Theory: the chaos in space
and the chaos in time.  A system whose configuration is capable of changing
with time is known as a "Dynamical System" (the WWW can be thought as a
Dynamical System). A Dynamical System consists of some "variables" and some
"equations of motion" or "dynamical equations". The variables are any things
which can vary with time (in this case, the variables can be thought as the
resources). They can be multiple or single, continuous or discrete. They
must be chosen in such a way that complete knowledge of all the variables
determines uniquely the "state" of the system at one time.  The set of all
possible values of the variables, i.e. the set of all possible states of the
system, is called the "phase space". The present state of the system is one
point in phase space. As time proceeds, this point moves in phase space. The
job
of the equations of motion is to determine how it moves. Given the present
state of the system in phase space, the equations of motion tell you how you
can calculate the state at the next instant of time. As time evolves, this
point describes a "trajectory" or an "orbit"
in phase space. If you know how to calculate this trajectory, you say that
you have solved the equations of motion. Usually, you are given the state of
the system at some initial time; this is called the "initial conditions".
Then you try to calculate the trajectory which follows from these initial
conditions...[2]

  Although I'm no expert on this subject (The Chaos Theory), there are some
people, like Dan Connolly, whos research interests are investigating the
value of formal descriptions of chaotic systems like the Web [3].  Maybe
this can be a startup for a section on the technical report, to describe
this interesting subject. :-)

3) Because of the topics that covers this technical report, I think that it
is an important academical source of information to the public.  Thus, in
the section 1.1.1 (Audience of this Document) [4], it's necessary to include
the academic community.

Cheers,

Sergio Rodríguez.

[1] http://www.w3.org/TR/webarch/
[2] "Chaos, Complexity, and Entropy (A physics talk for non-physicists)".
Michel Baranger.  Center for Theoretical Physics, Laboratory for Nuclear
Science and Department of Physics Massachusetts Institute of Technology,
Cambridge, MA 02139, USA and New England Complex Systems Institute,
Cambridge, MA 02138, USA.  MIT-CTP-3112.
[3] http://www.w3.org/People/all#connolly
[4] http://www.w3.org/TR/webarch/#about

Received on Tuesday, 13 January 2004 13:29:14 UTC