I am having an interesting conversation with Howard Bloom, author, memeticist, historian, scientist, and social theorist. We have been discussing network models of the universe and the underlying "metapatterns" that seem to unfold at every level of scale. Below is my reply to his recent note, followed by his note which is extremely well written and interesting...
From: Nova Spivack
To: Howard Bloom
Subject: Re: Graph Automata -- Is the Universe Similar to a Social Network?
Howard, what a great reply!
Indeed the metapattern you point out seems to happen at all levels of scale. I am looking for the underlying Rule that generates this on abstract graphs -- networks of nodes and arcs.
In thinking about this further, I think we live in a "Social Universe." What binds the universe together, and causes all structure and dynamics at every level of scale, is communication along relationships. Communication takes place via relationships. And relationships in turn develop based on the communication that takes place across them.
Relationships and communications take place between locations in the manifold of spacetime, as well as between fundamental particles, cells, people, ideas, network devices, belief systems, organizations, economies, civilizations, ecosystems, heavenly bodies, galaxies, superclusters, or entire universes. Whether you call it "gravitation" and "repulsion" and other forces are really just emergent properties of the dynamics of relationships and communications. It's really all very self-similar.
I believe that we can make an abstract model of this -- just a graph comprised of nodes connected by arcs -- where the nodes (and possibly the arcs too) have states, and information may travel across them. Then, at each moment in time, we may apply simple local rules to modify the states of nodes and arcs in this network based on their previous states and the states of their neighbors.
For example, at time t+1, the state of each node is a function of the states of the nodes within some number of arcs from it and states of the arcs along each path to each of those nodes. Also, at time t+1, the state of each arc is a function of the states of the nodes it connects and perhaps also the states of the arcs of those nodes.
A node represents an entity -- for example a particle or a person or a stock symbol. The state of a node can be a single number or an array of numbers representing many different variables, depending on our simulation. Arcs represent communications channels, through which nodes measure one another. The state of each arc encodes the strength of the relationship -- the communication channel -- it represents. Measurements can only happen via relationships -- for a measurement to take place some information must travel from the thing being measured to the thing that measures it. In my abstract model I use a directed graph -- so each relationship (arc) is only one-way from one node to another node. Thus a "bidirectional relationship" is a case where two nodes, x and y, are connected by two arcs xy and yx.
I also start with a maximally connected graph -- every single node has one relationship arc to every other node and one from every other node. This allows for every node to potentially make a relative measurement of every other node according to its "perspective" on the relationship.
At every step in the simulation, every node x measures the state of every other node y via the relationship from that other node y to x -- but the measurement is conditioned by the state of the arc along which it takes place such that in some cases it is enahnced dramatically, or dampened to the point where it is simply not strong enough to matter. When a measurement is dampened to that degree it is equivalent to there being "no relationship" between the nodes.
Thus although there are always virtual relationships between all entities, only some relationships are "actual" in the sense that they are strong enough to enable measurement to take place. And this changes over time, based on how the entities interact. Our rule should evolve the strength of relationships based on the measurements that take place across them.
The philosophy of this model is based on the insight that a relationship is in fact the most fundamental thing in the universe -- even more fundamental than particles or locations in space-time. This is very much philosophically in the camp of Liebniz as opposed to Newton.
In fact, in my model, both nodes and arcs are actually relationships -- a "node" is represented by an arc that loops back on itself -- it is something that measures itself -- a circular relationship; an arc is a relationship that does not loop back on itself -- a relationship that connects one node to another. Therefore there are really just relationships in this model but they are interpreted differently depending on their shape -- an "entity" is a node, a self-relationship, a communication channel is an arc -- an other-relationship. I mention this only because of its elegance -- it makes it possible ultimately to have a single rule that operates only on arcs at each step in the simulation (since nodes are arcs too in this conception), rather than having different rules to compute node states and arc states.
The most basic act in the universe is to measure something via a relationship. A measurement is therefore the most fundamental unit of communication. A series of measurements that take place between two entities is an interaction -- a process of communication. Relationships are communication channels (arcs) that affect the measurements that travel across them: strong channels may enhance measurements, weak ones may dampen them. So the measurements that nodes make of each other are conditioned by the arcs that mediate them. Likewise, the state of a relationship, and therefore its effectiveness as a communication channel, may change based on the measurements that take place across it over time.
This model is essentially very similar to a neural network, and in fact a modified neural network algorithm may be just what we are looking for. I would not be surprised if in fact we could empirically discover this rule by looking for a pattern in the way relationships and interactions develop among neurons in the brain, people in social networks, memes in belief systems, services on the Internet, stocks in economies, stars in galaxies, etc. As you point out, gravitation between stars is similar to the attraction between people. And relationships between people are not so different from topological connections between locations in space-time, or the forces that bind particles together.
Using networks to model these various phenomena is not merely interesting, it may be essential to discovering a unified theory of the universe -- there may actually be a metapattern to all "social networks" that helps us to discover the key underlying laws of the universe, at every level of scale. And that is something our civilization has not done yet -- we have not found a general theory of structure and dynamics that applies equally well at every level of scale, in every context. Quantum mechanics is still not unified with Relativity, let alone with Biology, Society, Ecology, Economics, etc.
I think this "metaunification" will be easier to accomplish if we use the same basic model to represent structure and dynamics at every level of scale. Currently very different models and languages are used by thinkers to represent systems at different levels of scale -- and this is one of the reasons we have not achieved much unification to date. We need to get everyone speaking the same language -- using the same modelling tools -- so it is easier to map between discoveries in different domains. Network models are ideal for this purpose.
I believe that an empirical study of existing social networks on different levels of scale is one route to finding the general pattern we are looking for: All social networks -- at all levels of scale -- should obey certain laws that we can discover through observation and then generalize into a general theory. Another approach is purely through mathematics -- it should be possible to derive an abstract mathematics of social networks. Finally there is also the computational approach -- simply generate and test different social network rules, and perhaps even use a genetic algorithm to evolve an optimal one. Perhaps that is the computation that our universe is running?
--- Nova Spivack
From: Howard Bloom
To: Nova Spivack
Subject: Re: Graph Automata -- Is the Universe Similar to a Social Network?
Nova--Fancy running into you here on paleopsych, The International Paleopsychology Project email list.
Pavel Kurakin and I, curiously enough, are looking at the basic patterns underlying social connections among quantum particles, insects, and, implicitly, humans for an upcoming paper. Pavel is with the Keldysh Institute of Applied Mathematics of the Russian Academy of Science.
Something you've said hits a nerve: "the network seeks to help each node optimally balance its connectivity against information overload". Bear with me while I seem to go way out beyond left field. I'm working on a book called Reinventing Capitalism: Putting Soul In the Machine--A Quick Re-Vision of Western History. One of the chapters is called "Marketing Meaning—Moses And The Slogan".
It's about the way in which Moses marketed his new religion...the way in which he drummed it into the head of his Chosen People. If you can believe the Bible and Sigmund Freud's brilliant analysis of Moses and of the basics of community building in his Moses and Monotheism, Moses boiled his entire system of belief down to a slogan--"Hear, oh Israel, the Lord The God, the Lord is one." Then the sociologically wise prophet told his followers to hang this bumper-sticker distillation on their doorposts so they would see it in the morning when they walked out of the house and in the evening when they walked back in again. He ordered the men to bind the slogan to their wrists, arms, and foreheads twice a day. And he apparently made darned sure that this catch-phrase was repeated a lot.
Today we call this sort of thing branding. Why is it so necessary to us human beings? Why do we need to have just a small Olympus of stars and leaders we can gossip about? Why do we focus on brands like Coke, Pepsi, and Dr. Pepper, but toss lesser known brands aside? Why do we show interest in only two or three presidential primary candidates--Kerry, Dean, and Clark--much to the consternation of the other five or six?
We have only seven slots for immediate memory in the brain. This limits the information we can handle. It limits the number of choices we can comprehend..or tolerate. (From the description of another Reinventing Capitalism chapter: "A little choice is freedom. Too much choice is agony.")
So to get through to us, you have to make it simple and you have to make it stick. You have to repeat it over and over again until we get it. Once we've gotten it, we can slide it from consciousness to habit (from explicit memory to implicit memory) and concentrate on something else.
What does this cellular automata-style rule of individual capacity mean when writ large in group behavior? It means that we need to do a lot of quorum sensing. We need to go along with the herd. We need to pay attention to what everyone else is paying attention to. We need to buck it and criticize it if we want, but to fixate on it one way or the other. If George Bush Jr and the Iraq War are the topics of the day, we can hate Bush, love Bush, hate the war, love the war, but not get sidetracked by detailed examinations of who the Chechen rebels are.
We go with the flow of popularity. We follow fads, even if we only come along for the ride and criticize them.
This rule pretty much applies to the cosmos, too. Gas whisps and dust clouds in the early cosmos went where the action was. They congregated around self-forming swirls called galaxies. Then they aggregated even further in suns and planets. The general rule was this: To he who hath it shall be given. From he who hath not, even what he hath shall be taken away.
Why the repetition of this rule on two very different levels--the gravity wars that led to galaxy formation and the popularity wars, the wars of social gravity, that determine who will be the candidates in a presidential election and who will be the hot rock and TV stars of the day? Humans aggregate to limit the flow of information. But do specks of interstellar dust interpret information, too?
Specks of dust do respond to attraction and repulsion cues. If they're negatively charged they avoid other negatively charged things. They move in the patterns dictated by magnetic waves surrounding stars and furling in galaxies. And, of course, they pick up on the come-hither cues of gravity.
But surely interstellar dust flecks and whisps of gas can't work to optimize their information flow. They can't gravitate around stars because of a need to keep their seven slots of memory from radical overflow. Nor can they use those stars to keep them entertained--to assure that they don't suffer the pain of boredom that comes from information underload.
Whither comes this common pattern that keeps the big getting bigger yet provides a few key choices? Why do embryonic stars in a star nest or cluster compete like starlets in Hollywood to become the next big center of attraction?
There's a primal pattern, an evolutionarily stable strategy, what I've been calling an Ur-pattern, rearing its head here on many levels of emergence. But how does this similarity appear and why?