I am sort of coming around to my original position. The non-hierarchical nature of the software at its core, has to be acknowledged. You can't just say it's a hierarchy because that's how the packets flow. It's a lot different than a pure hierarchical network. — fishfry
It might be helpful to talk about this in the language that network theory has created for itself.
In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks. The uprise of hubs in scale-free networks is associated with power-law distribution. Hubs have a significant impact on the network topology. Hubs can be found in many real networks, such as the brain or the Internet.
https://en.wikipedia.org/wiki/Hub_(network_science)
So your peer-to-peer revolution created a flat landscape - a new world in which making an informational connection carried a uniform costs, regardless of the underlying hardware physics.
But then that flat landscape got colonised in a free or locally unconstrained way. Everyone got busy on the internet in ways that freely expressed their own functional(?) human interest.
Connections were added and a hierarchical structure resulted because of the Matthew Effect or preferential attachment. Hubs and fat tails became a thing.
A "flat" network would have had a Gaussian randomness in its connectivity - everyone would have connected to the same average degree. That is what net equality would have looked like.
But as a freely growing beast, the internet instead developed hierarchical complexity. It developed the different statistical pattern of scale invariance. It became fractally organised so that now scales of being were themselves "equalised" in that there was no one standard mean. Connectivity was powerlaw and hubs of any size could manifest.
Porn could dominate the internet. And philosophy forums could live alongside just as freely as the tiniest scales of interest communities.
Well, on technical point, the internet is probably more log/normal as a distribution and not quite making the giddy heights of a log/log distribution. Just like the stock market or most other real world systems.
So the Gaussian and Powerlaw models of "randomness" are a dialectic that frame the ideal extremes of self-organisation. Reality falls in-between the two, depending on how constrained or unconstrained the connectivity happens to be.
But the point is that hierarchies of connectivity emerge naturally as the structures that dissipate flows. And this is dialectical in the sense that either the flow tends towards the closed Gaussian equilibrium balance, or towards the exponentially growing Powerlaw equilibrium balance.
A Gaussian hierarchy is canonically simple. It is a single scale system because it has a single mean. Like an ideal gas, it has a stable temperature and pressure - even as all the gas particles ricochet about with statistical freedom. There are no internal scales of difference - gangs of particles that dominate. Everything is as average as possible. Internally there are no differences that make a difference, even if every particle is expressing some different momentum.
Then a Powerlaw system would be at the other extreme. As
Universality describes, as you start to disrupt the stable Gaussian equilibrium of some flow by heating it up, it start to form internal structure.
You get the dialectical patterning that Banno stumbled upon when he hastily googled "What is self organisation"...
pigmentation of a porphyry olive shell
lichen growth
zebra and giraffe coat patterns
hexagonal Bénard convection cells
spiral patterns produced by the Belousov-Zhabotinski reaction — Banno
If an equilibrium balance is disturbed by an injection of energy, then it starts to oscillate. The system depends on some dissipative balance of reaction~diffusion and suddenly it is having to absorb more energy than it can immediately handle. It becomes like the straight river that begins to carve out a snaking channel. If the river can't drain faster, it can add dissipative capacity by becoming longer. And so it does.
But keep adding energy and there is a transition to chaos - a Powerlaw regime. Dissipative features - oscillations, turbulence, etc - start to appear on all scales as ways to absorb the increasing throughput. You again have a scalefree hierarchy of structure being expressed on every possible scale to cope with the demand. You arrive at an ecosystem level of complexity in biological terms.
So the patterns of nature take these forms. You have the highly Gaussian pole of being where the hierarchy is just a simple stable bounded system with no internal structure.
In human terms, we might be thinking of ideals like a hunter gatherer tribe or a Masonic lodge - a group with a stable common identity and no internal divisions. (Of course, no actual tribe or lodge is ideal as stuff is always happening to disrupt the "energy").
Then at the other extreme of being, you have the crazy chaos of the stock market or the internet. You have some essential dialectic - such as reaction~diffusion - being expressed over all possible scales of being. Internally, the number of hierarchical levels tends towards the infinite.
In terms of wealth vs poverty, or fame vs anonymity, these social systems have such diversity of outcomes that anything is possible in either direction. Life isn't homogenous as it is with a static hierarchical order - a single scale of local~global interaction, a single deal when it comes to the exchange between competitive and cooperative behaviours. It is instead as inhomogenous as could be imagined .... and yet still a stable, natural, functional, outcome in terms of producing the maximum dissipative flow that its structure can support.
Chaos as a dialectic expressed freely over infinite scale is also a hierarchical state of order.
And then - because we have these two ideal limit descriptions of hierarchical order - we also have all the intermediate states that are somewhere in between. We have the log/normal conditions where there is a fair bit of hubbing, but a fair bit of egalatarianism too. And this might be a functional balance for dealing with the available entropic throughput - doing the actual job of the system.
Not every river has to be a sluggish canal or a wild fractal delta. Plenty are carving out snaking loops across the landscape as an intermediate form of hierarchical architecture.
And here endeth another science lesson on how it all connects up.
:grin: