Fascinating paper. Seems to support the idea that social networks are just another species of complex system, and as such tend to develop self-reinforcing structures of influence according to an underlying set of universal state-transfer properties, iterating over time and amplifying the quantum effects governing atomic interactions between members of the ground set of elements (people, at this scale), broadly similar to the way that complex physical systems are all echoes of thermodynamics.
I wonder... will there be a periodic table of ecosystemic elements some day, a Zuckerberg's standard model of quantum sociodynamics? /s
Also could suggest that by mandating periodic group-connection-reinforcing rituals, like daily/weeky religious or other activity, that a society can reach a connectivity state that's quite inflexible.
Indeed, this is a function of monumentalism, which is to reify and consolidate ritual into a pattern that is as permanent and immutable as humanly possible, and thus make the physical landscape shared by a given community reflect the mental landscape they likewise share.
keeping in mind that certain forms of inflexibility are vital to the structure of an organism. Bones for example. Or in the case of the human super organism, ecological stewardship, which was the original subject of the religious sciences.
I can't believe this is a published article. 3/4 of the paper is essentially crackpottery (e.g. Proposition 5 proves that the composition of surjective maps is surjective), while the final 1/4 is a "proof by picture" (see Figure 6) that you'd see from a mediocre undergraduate pset.
Proposition 5 proves that the composition of surjective maps are _necessarily_ surjective only when the second map is monotone continuous. Based on the definition of surjectivity given, you can have a composition of surjective maps that isn't surjective.
The figures ("pictures") aren't part of the proof, they're part of the presentation, and Figure 6, as stated in the paper, is included as a reference to an analogous work.
If you read the last 1/4 of the paper, you'll see that Figure 6 is an integral part of the discussion; furthermore, nothing in the discussion is proven rigorously --- they all appeal to the picture.
You don't need a PhD in mathematics. Firstly, they explain the (already existing) concept of a closure (think for example transitive closure, which seems to be exactly what they're going for).
Y.ϕ is a notation that means we apply operator ϕ on Y. It seems like they work with a closure operator that goes akin to "if we have a graph G where A relates to B and B relates to C, then G.ϕ additionally has A relating to C".
Then they look at how a social network evolves under the (formalized) assumption that no two individuals become one individual. Then they prove, under this condition, that, as the network evolves, some separate sets remain separate. That is, certain structures in the graph remain stable.
That's a broad overview, I think. I only spent like 15 minutes reading and writing this, so I might be mistaken.
The math is tough to grok, but it appears they are using some set constructions to show that given a certain cycle size (4 or more) within a graph, those cycles are stable (Irreducible) based on some previous work. Thus, network stability is contingent on those cycles and you can extend this to say that the reason social networks don't dissolve is because these subsets give stability to the graph?
Honestly, I've had easier times reading through representation theory concerning quantum mechanics! I think I see what it's trying to say though, which appears to be some mathematical basis for what we experience online; communities form, fragment, and it's exceedingly difficult to halt or reverse that process of fragmentation and isolation. Eventually, this trend results in the decoherence of the network.
Not sure this accounts for the fact that social networks, unlike galaxies or the universe can be folded and reconstituted at will. If you think of it like making a pizza, you spin the dough and as it spins it will eventually break apart (mySpace, Tumblr, your-favorite-forum-of-yore) but you can always fold it back over itself. In this metaphor, Facebook's introduction of new features and its acquisition of Instagram, WhatsApp and forthcoming VR (in a way its own universe, without any natural law like entropy) represent folding - reconstitutions and renewals. I suppose we can conclude that if entropy represents a fundamental part of natural law applicable to social networks, our technology will try to negate and dominate it. At the very least and assuming the thesis of the paper to hold true we can say, Social Networks are doing something about it.
whenever there is gradient between [energy] potentials the things would move along it to neutralize the difference - that is the entropy law at work, nothing happens without it. Folding back, reconstitution, renewal - it is all requires expending energy, ie. entropy increase.
> if entropy represents a fundamental part of natural law applicable to social networks, our technology will try to negate and dominate it.
our technology is just a tool of ours. Being live organisms we follow the main principle (stemming from the 2nd law) what the life is built upon - negating and dominating entropy in some small volume of spacetime by using energy obtained by increasing entropy in some other volume of spacetime by even larger amount than the energy extracted and the entropy dominated/negated. Technology just allows to amplify that process.
I wonder... will there be a periodic table of ecosystemic elements some day, a Zuckerberg's standard model of quantum sociodynamics? /s