none of this is really original thought but i think its probably useful for my reference to keep all these things and the associated eponymous laws in one place
the value of a network grows as the square of the number of endpoints because of triangular numbers— metcalfe’s law
but most networks aren’t fully connected, because with human social relationships— dunbar’s number caps the degree at 150
however beyond friendships, which can be thought of as bidirectional graph links, there are also celebrities manifesting as asymmetries in the in and out degree burgers. this means that informational paths aren’t quite symmetrical because certain nodes are capable of reaching a larger audience in a given path radius.
this leads to a different sense of value for the different nodes, and this establishes different classes
but beyond mere celebrities, which are kind of the extreme end of the asymmetry, there are also nodes which have exceptionally high degrees and others with lower ones, giving the entire network an element of the hub-and-spoke topology, which can route things quite efficiently.
this means that the average path length (bounded by network diameter) between any two nodes can be approximated as log(n)/log(150) which is almost always a rather small number— cf. global village, milgram small world, six degrees of kevin bacon,
however, social network topologies aren’t normally randomly connected, they usually reflect some geographic distribution with a few random links. people are connected at different levels and at different densities through their local neighborhoods, high schools, colleges, jobs, and each can reflect a different spatial scale, town, counties, states, countries, etc. with relatively little knowledge about the structure of global geography, people can exploit these generalities and sparse connections to route information to arbitrary others
but importantly, paths are also attenuated and amplified by the bandwidth of their carriers. messages which travel long distances tend to be smaller because they are bottlenecked by congestion caused by overloaded switches and infrastructural links
but bandwidth is a deeper concept than communication infrastructure because it’s the fundamental difference between written language, speech, video multimedia, holography, gestures, user interfaces and the ultimate goal, which is interacting directly with brains
because the interpretation of the system as a network spans not only the macro scale agglomeration of minds, but also the internal representations within people of thoughts and ideas.
the mind, as a solid block of matter has an extremely high bandwidth connection within itself but then communication with other ideas is blocked by the low bandwidth and asymmetric process of human communication and interaction
note that i’m conflating bandwidth and information density in spite of the fact that they are actually quite meaningfully distinct
in terms of sensory apparati and the associated neural processing capacity, the highest bandwidth is almost certainly visual, followed by audio, then tactile followed by gustatory and olfactory.
information density pertains to a coding scheme for information which is modulated over one of these underlying senses as a carrier. for visual, this means hand gestures as well as the written word. for audio, this means speech as well as sounds.
the last two bits were dealing specifically with ingress, which uses senses, but egress is another half. people can emit auditory signals with voices, and interact with the world by pushing buttons, pulling levers, and waving arms or by changing their physical location by walking around.
vocal cords can carry spoken language as well as simpler grunts. there are some highly structured languages that can be coded in the form of gestures as well, but there are also simpler hand gestures.
just as communication isn’t limited to the space between people, but also the space inside, the targets and senders need not be human, for they can be inanimate or otherwise nonsentient— communicating to a stick or a shovel, or a computer intelligence or lack thereof
what is the point of all of this? basically to say that the value which arises from a network of humans grows not just as the square of n, but also with the bandwidth of the links
so how can you kind of visualize this? i guess you can imagine the average length of paths in the network as a metric which reflects the level of obstruction for the flow of information, kind of like resistance in electrical circuits
if one increases the bandwidth between links, thus bringing people closer together, the network becomes more more valuable by a factor of its average path length.