Saturday, March 03, 2007

The fractal nature of the Web - updated

TBL has updated his commentary entitled "The Fractal nature of the Web" with some notes on how the Semantic Web can and must work with a combination of overlapping global and local ontologies. He discusses the importance of thinking about ontologies and domains from the perspective of agents that communicate with messages relating to ontologies and domains that they share. He concludes:

So the idea is that in any one message, some of the terms will be from a global ontology, some from subdomains. The amount of data which can be reused by another agent will depend on how many communities they have in common, how many ontologies they share.

In other words, one global ontology is not a solution to the problem, and a local subdomain is not a solution either. But if each agent has uses a mix of a few ontologies of different scale, that is forms a global solution to the problem.

His overall "web fractal" commentary starts from this thought:

I have discussed elsewhere how we must avoid the two opposite social deaths of a global monoculture and a set of isolated cults, and how the fractal patterns found in nature seem to present themselves as a good compromise. It seems that the compromise between stability and diversity is served by there the same amount of structure at all scales. I have no mathematical theory to demonstrate that this is an optimization of some metric for the resilience of society and its effectiveness as an organism, nor have I even that metric. (Mail me if you do!)

However, it seems from experience that groups are stable when they have a set of peers, when they have a substructure. Neither the set of peers nor the substructure must involve huge numbers, as groups cannot "scale", that is, work effectively with a very large number of liaisons with peers, or when composed as a set of a very large number of parts. If this is the case then by induction there must be a continuum of group sizes from the vary largest to the very smallest.

File this under "food for thought." This issue of how domains can interoperate and the respective role of global domains is key to developing a global knowledge web. How to achieve stability in the presence of diversity is a quite difficult problem. This will need some original thinking on the nature of equilibrium.

-- Jack Krupansky

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