Phil > > Do you know anyone else working on this? I have been "noodling" on it for some time. Nothing published exactly. > > > In thinking over what the measure of 'distance' between nodes in > networks means (the nominally 5 degrees of separation for people and > 19 degrees for web pages) it's occurred to me there are two very > different sides of connection. Natural system networks tend to be > exceptionally well connected *as a whole* , but the trade-off is that > their sub-nets become exceptionally self-centered *as parts*. > Thinking of highly connected nodes as 'hubs' explains how large > complex systems can work as a whole, but thinking of the regions they > connect as 'hives' explains how they can retain their independence as > parts. I'm not sure how Hubs and Hives connect in your analogy. Airports are Hubs and cities are Hives... if I understand your meaning. I assume you are describing regional (relative) self-sufficiency with high internal connectivity (everyone in a small town knows everyone else) vs intra-regional connections (highway systems or airlines) which have a very high valency (number of travelers using a given entrance/exit ramp or airport).
> What we seem to have in the scale-free design of natural systems > is also new evidence of how nature operates with lots of 'different > worlds'. You are referring to the emergence of heirarchy in these systems (villages eventually connect into networks of villages/widely distributed rurals cluster to form regional centers/villages?) > One opportunity that presents is a way to find the > functional boundaries of independent system parts topologically. Yes, this is where I have been noodling mostly. The form/function duality. By noticing the structural decomposition of a "system", one can maybe identify the subsystems within a system of systems. I have observed this on at least two "engineered" systems... a The first was a ~5000 node dynamical systems model of 17 infrastructures built by dozens of individuals separately but with external references to other infrastructures. Taken as a whole, the graph of this coupled dynamical system is a big hairball until one teases things apart a little more using clever graph layout techniques. The result in my case is that the subsystems (not surprisingly) could be identified by their relatively high intersubsystem connectivity vs their relatively low intra-subsystem connectivity. The second is the Gene Ontology. We used a variation on the same graph layout tools to cause the highly interconnected nodes to cluster together and the less intraconnected clusters to separate. > Not the least benefit would be to help us discover the correct ways > to aggregate our data for other things. By using a modified (general/tunable) spring model, we were able to get the data to "self-aggregate" in ways that exposed the structure. Both systems were somewhat engineered (models of infrastructures built by humans and knowledge map of genetics) but described somewhat more natural systems (the union of all infrastructures recognized in 1st world human cultures, and the various genes responsible for important/common function in all studied life). > > The information boundaries surrounding self-connected parts of whole > systems also seem to define structural limits for the 'world views' > for things looking out from their insides. I'm not sure I know what you mean by "structural limits"... in the case of geospatial distributions of humans, the literal spatial separation between "villages" or "cities" tends to attenuate awareness of the "things" on the other end of the connection. Illustrating (or contradicting that), Santa Fe has(Had) roads named "old pecos trail", "taos highway", "cerillos road" which were descriptive of the community in which you would find yourself eventually if you took that road. Am I understanding (or illuminating or confounding) your point? > While the system as a whole may be well connected, those global > connections would naturally tend to be hidden for observers building > their own world view from within its locally well connected parts. Like I buy a bag of salad at the produce dept of my local grocery, hardly thinking about the distribution warehouse (maybe) in Albuquerque where trucks from TX, MX, CA, AZ arrive with all sorts of produce, sort it out, bring it to the back door of my market, etc... ? W > > I've been trying to explain my observation that the world views of > people are often exceptionally different, and yet we remain largely > unaware of it, mostly ignore it in conversation, and are relatively > uninterested in the deep communication problem it produces. In this, I hear you saying that people partition the graph of their life differently? That in the above-described method of aggregation, we use different edge parameters to aggregate what we consider to be part of our "hive" and what is only accessible through another hub? My parents use their computer/internet as a "hub"while many of us here use it as a "hive"? One person's metric of distance might be "how long does it take me to get there?" while another's might be "how much does it cost me in $$ to get there?" while another might consider "how far is that as the proverbial crow flies?", and another "how much irritation will I go through on the way there?" The shift from 55 to 70+ freeway speeds made me newly aware of this... instead of driving to Denver on the back roads (at an easy 60-65 mph) vs the freeway at similar speeds, it is now more efficient in time to drive the (longer) freeway at 75-80 vs the back roads at 60-65 still. The back roads afford better scenery and more entertaining places to stop... but the freeway affords the use of cruise-control and regularly provided stops with name-brand eateries. Which is "closer"? > I have a list of other 'good reasons', but if it's a natural > consequence of the scale-free topology of natural system > networks, that could explain a lot about why humans so regularly fail > to communicate but think they do. I'm still missing something here I think. > That our individual understandings of 'the universe' develop in > relation to sub-networks having local information horizons in every > direction, it means every 'hive' looks like the 'whole'. I do think I know what you are describing here, that the natural scale of human perception, when used as a theshold to the scale-free networks of relations they inhabit, yield a set of "separate worlds"... Are you also noticing that different people have different qualitative perceptions (value systems) can live in different worlds whilst sharing the same space (physical and logical)? This is what I want to attribute to self-organized graph layout using different parameters of the edges. > When real complex systems also cross-connect many kinds of local > networks at once (environment, work, family, community, friendships, > beliefs, interests, etc.) it adds completeness to the natural > topological 'illusion'. Can you rephrase what you mean by "topological 'illusion'"? I think I'm "in the same universe" as you on this but naturally not completely. > Perhaps the very 'independence' of our world views is further > evidence of how deeply embedded in a larger system they are. Perhaps. Quantitatively large as well as qualitatively. Not just large graphs of graphs, but multi-graphs wherein the power-law of valency varies over the "type" of edge being considered. Everyone is one-degree of separation apart by this e-mail list, but more like 2 or even 3 by personal connection. I have never met you and perhaps of the other FRIAMers I have met, none of them have met you either (though I suspect Gueren to be a bit of a hub in this regard). Our "co-citation" distance is probably at least 3 and probably 4 or more. > > Does that make sense? Maybe! It depends on what world you live in! - Steve ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
