From: Bullard, Claude L (Len) <clbullar@ingr.com>

Date: Tue, 13 Jan 2004 12:47:09 -0600

Message-ID: <15725CF6AFE2F34DB8A5B4770B7334EE03F9F130@hq1.pcmail.ingr.com>

To: 'Sergio Rodriguez' <srodriguez@bdgsa.net>, ''WWW-TAG' ' <www-tag@w3.org>

Date: Tue, 13 Jan 2004 12:47:09 -0600

Message-ID: <15725CF6AFE2F34DB8A5B4770B7334EE03F9F130@hq1.pcmail.ingr.com>

To: 'Sergio Rodriguez' <srodriguez@bdgsa.net>, ''WWW-TAG' ' <www-tag@w3.org>

And as a dynamic system, it *behaves* as an amplifier which is its chief peril and application. An investigation pertinent to those interested in the NLDS line of thinking is which patterns of behavior lead to stable systems and which lead to strange attractors. The power law aspects of web linking are already proven. The problem Berners-Lee outlines has aspects of noise in a networked system of systems. When one amplifies noise, it just gets noisier. Should the solution to the XML-As-Stable-Value (invariant to transformation by multiple systems) problem be opportunistic/adaptive or fixed? Because this thread itself can be unstable, it might best be taken to XML-Dev where it is already underway. len -----Original Message----- From: Sergio Rodriguez [mailto:srodriguez@bdgsa.net] Sent: Tuesday, January 13, 2004 12:29 PM To: ''WWW-TAG' ' Subject: 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 Rodriguez. [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/#aboutReceived on Tuesday, 13 January 2004 13:47:10 UTC

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