> 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.
Well, the intense 'hive' of relationships between airline attendants at an airline 'hub' also counts, though they appear at different levels of the airline network organization. A lot of the appearance of things has to do with how you aggregate your data. There probably are also a number of more regional airline networks that are a 'hive' of sorts that then serve 'hubs' of a larger system, like bush flights in Alaska that would normally just 'not count' or for which data would be unavailable when drawing the shape of the larger network. > 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). right, and the relative independence of what happens inside a 'hive' and how it forms a 'world of its own'. > > > 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?) Well, not quite. The inception of the idea was more that what's different between a mean distance in a network of 5 degrees of separation between people, and 19 degrees when measuring the distance between web pages, seems to indicate that the separation between our mental worlds is vastly greater than our separations physically. The marvel is that when we walk down the street we're quite unaware that many of the worlds of ideas in other people's minds you'd a need to go to vast lengths to translate. The scale free property that yields a high degree of connection for the whole network also yields a high degree of isolation/independence of the parts. > > 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 started doing that by identifying a system 'form' as growth and then using that as a way to aggregate the locally involved network identified with the same process, then locating various working parts needed for the complex process. I think that's a great method for some things, but a statistical measure, a topology of 'hiveness', might be better for the vast databases that are prevalent. I've not been able to assemble a network modeling and analysis tool kit for myself yet, for several reasons, but I can see natural systems comprise networks of physical parts that are diversely cross connected on many levels, forming self-organizing cells with extensive local interconnection and sparse remote connection. Sometimes network maps wouldn't show the 'hive' characteristic of natural systems when mapping 'nodes' as categories of things, rather than individual physical ones. If you map internet nodes as 'cities', for example, you'll still get the scale free distribution of connections, but no 'hives', because of how the data is aggregated. > 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). I'm not quite following what the network is composed of, or what physical system it is embedded in. > > > > 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. When in New York everything is interpreted in relation to the 'hive' of New York issues, and similarly when up camping in the mountains. It's one of the great pleasures of 'going places' that you get to switch the whole context of your thinking for a while. The idea of structural limits is that either of these 'places' is defined by it's strongly inter-connected connections and that that has an interior and edges. As we go out to the edge of the domain of any 'hive' of connections, I think we most often turn back, since what's beyond looks like nothing, since it has no role in the hive. When you're out in the woods the idea of 'ordering out Chinese' is very far from reality and in the city spitting on your knife and rubbing it on your pants before sitting down in the dirt for dinner probably wouldn't occur to you either. How many worlds can a mind switch to? Maybe a large number, and there's just no telling what one in active in anyone else's at any given time. ;-) I guess it looks like I'm poking around with the absence of complex local mesh like regions with their defining circular connections that are so prevalent in nature but not prominent in either the discussion or displays of most network maps. > > 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... ? Sure, the 'little world' of the shop may have a very special community of issues that buzz around it and occupy all the people that pass through as consumers, and you don't see where the salad greens come from any more than you see what the truck driver does with the cash that somehow gets from your pocket into his. When you treat the shop as a 'node' you get an image of the larger scale system structures, but they only function because the shop is also a 'hive'. At the larger scale the chatter between the truckers may become a 'hive' of relations that itself could then relate to other things as a 'node'. 'Hives' and 'nodes' may often be the same thing, looked at differently. > > > > 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? Or that the 'hives' of relationships that we are in the middle of, look as if they are the whole world, but are really only complete and satisfying within themselves, and not actually the whole world. Thus the potential for illusion, and people living in literally different worlds of ideas and both having to make allowances for how idiotic the other must surely be. My goal would be to reduce the problem to the one you suggest, at least learn some way to recognize what local world I'm speaking from and to, avoiding the complete structural disconnect problem so there's just the matter of two perspectives of the same thing. > 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"? They all sound like good measures to me, so long as you're using the same one. > > 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"... It's forming an idea that scale free networks allow clusters to have both tight internal connections with independent behaviors, while also participating in larger systems to which the cluster is connected by some group of its parts as hubs. The thought is that observers within such a cluster, human or other type of 'exploring system', might naturally see the cluster as the whole world just because clusters tend to have edges in all directions. Perhaps some clusters might look more like the 'whole' world if the links to other things were like that between the trucker and the vegetable shop, as through-put, physically connected through it but not participating in the hive of the activity at all. > > 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. But what sort of data would reflect such things? > > 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'm just referring to the possible appearance that there is nothing beyond the 'hive', because when within a 'hive' of connections you the strength of it's connections has boundaries in all directions, sort of like a 'niche' within which a fall-off in connections is read as the end of the world. I also think an observant person might notice secret exits from the hive, perhaps stopping to talk to the truck driver and learning a little something about the world beyond the vegetable shop, but that's making a break from the hive. > 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. The interesting thing about people is we all have different kinds of doors we open to each other at different times, lots seeming to have to do with finding links between world views we find are built so differently some times. Some of that is personal matters, and that everybody makes up their own, but there's also a part that comes from people not being aware of networks and that the world inside scale free networks seems it might look like a different world from inside every part. An email forum and it's conventions like this, might look rather strange to some, where people just throw all kinds of things out and occasionally there's a little fast paced flurry that follows, producing not so much more than a great accumulating kind of 'compost' to mull over it seems. > > > > > Does that make sense? > Maybe! It depends on what world you live in! yea! Phil > - 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
