The Network of the Universe

In the movie Signs, a former Episcopal priest played by Mel Gibson discovers crop circles in the fields on his farm. The crop circles are the first signs of an impending alien invasion. As the movie plays out, however, the real signs of the movie are events and misfortunes which seem to have no meaning at the time they occur. A driver falls asleep at exactly the right moment to run off the road and strike Mel Gibson’s wife. The wife’s last words as she dies pinned between the vehicle and a tree. The daughter’s obsession with filling glasses with water and leaving them around the house. The brother’s failed baseball career and a bat hung on the wall to celebrate a long home run. The son’s asthma which causes him to unable to breath as the alien tries to poison him with gas.

Although Signs is only a good (not great) movie, it is a movie I enjoy watching and re watching. The movie speaks to the great mystery of patterns in our lives and in the world – how things unfold and seemed to reveal their meaning over time.

In the Foreward to the Richard Wilhelm version of the I Ching, the ancient Chinese book used for fortune telling, Carl Jung attempted to come up with a theory of how the I Ching could actually work to provide guidance about the future. The concept he came up with he called “synchronicity”. The idea was that the hexagram thrown by the person consulting the oracle partook of the quality of the time at the moment. The connections between the person, the future, and the hexagram were not causal. In fact, they were “diametrically opposed to that of causality”. He thought there was some “peculiar interdependence of objective events among themselves as well as with the subjective (psychic) states of observer or observers.” (1)

Many years ago toward the end of my last year in college a lady and I needed to decide where we would go after school was over. Our choices were Colorado, Oregon, and Arkansas. We consulted the I Ching for each one. Oregon looked most promising so that was where we went. We saw some sort of meaning in a pattern found in the ancient Chinese book that was derived by throwing coins. Was our choice any better or worse than it might have been had we employed some more “logical” method? How subject to chance events in our past might the “logical” method had been?

The patterns and meanings of events in Signs spread out over time. The patterns of the I Ching extend from the present to the future. In both cases, meaning always comes from the observer.

I have little doubt that much of the meaning we seem to find in the world is in our brains and not necessarily in the world. A good part of what we believe to be meaningful is little more than coincidence or forgetfulness of contrary evidence. Michael Shermer talks in How We Believe (2) about humans as pattern seeking creatures. In most cases simple pattern matching serves well. A dropped rock falls and might hurt your foot if it lands on it. Prey run. Bright fruit is sweet and good to eat. Dropped rocks will fall but not in space. Not all prey run; some play possum. Some bright fruit is bitter and some is poisonous. The pattern matching works well most of the time but we have to temper this with experience and the possibility the pattern doesn’t work in every case. In a nutshell, this is what science does on the most sophisticated level.

Why does pattern matching work so well? Could it be that the world and our brain are constructed in a similar fashion? Wouldn’t our brain have to somehow mirror the external world in its structure? Is this why we find pattern, meaning, and order in the world?

In a study (3) published in November, scientists led by Dmitri Krioukov simulated the growth of the universe and discovered that “that the causal network representing the large-scale structure of space-time in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks.” They speculate that “some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive.” I must confess I can’t follow much of the mathematics of the study but an easily read account (4) of it can be found on the Time Magazine website. Matt Peckham writes: “Not only are we star-stuff, but that there may be a kind of cosmic feedback loop in the design of our brains and what we’ve created using them.”

We can think of a network in its broadest sense as a structure consisting of nodes and connections. A computer network consists of computers connected by wires or by wireless connections. A social network is people and groups connected by relationships. A single living cell is a network of complex organic molecules and signaling mechanisms to control metabolism and reproduction. Our brains are biological neural networks consisting of neurons connected by synapses. A key aspect of a network is that there is no hierarchical control. Order and structure seems to emerge at every point in the network often with the individual sub parts resembling the larger part or the whole. For example, relationships between individual within a group in a social network resemble the relationships between groups. In a network, causality cannot be determined. Every event determines every other event. The pattern and order of the network emerges from the initial state and the rules of the network.

What the Krioukov study shows is that the clustering of matter on a large scale in the universe mathematically looks like a network. If this is the case, then the organizing principles of the universe at the largest scale down to perhaps relatively small scales might be similar or perhaps even the same. Things as dissimilar as the Internet, galaxies, a living cell, and our brains may be organized by the same rules. This describes a fractal-like, self-similar world where the small and the big resemble each other.

Stuart Kauffman has studied extensively the role of networks in biological systems. In his book At Home in the Universe (5), he shows how what he calls “order for free” can emerge in networks without any predefined plan or hierarchical control through simple rules and constraints.

He asks the reader to imagine a network of three light bulbs with each light bulb having only one of two possible states, on or off. Each bulb receives input from the other two bulbs. He then assigns rules for each tick of the clock as to how the bulbs light based upon inputs: for example bulb 1 lights when both bulbs 2 and 3 light. Bulbs 2 and 3 light if either of their two inputs light. In this simple network, the pattern of bulbs lighting will eventually fall into some simple repeating pattern. The exact pattern depends upon the initial state. The light bulbs could become immediately stuck in a frozen pattern or they could execute the most complex pattern possible that allows the three bulbs to cycle through every one of the eight possible permutations. He then asked the reader to scale up the network of light bulbs to a thousand. Even this larger network might become stuck in a simple pattern depending upon its initial state. Astoundingly, if each click of the clock was a trillionth of a second and the network was stated in a state that allows it to cycle through all of its permutations, a cycle would not complete in the lifetime of the universe.

At the one extreme, we have a high degree of order but very uninteresting or frozen patterns. At the other, we have complexity so great that it appears random. We can have complete order, complete chaos, or something in between. Kauffman then shows is that by tuning various parameters in the network, the exact point at which order changes to chaos can be controlled. Life, he believes, operates at the edge of chaos. He says: “complex systems exist on, or in the ordered regime near, the edge of chaos is because evolution takes them there.” Life cannot evolve and change if it is stuck in a frozen, uninteresting pattern because it would have no flexibility. On the other hand, it cannot venture too close to the chaotic side because it would be unstable. To evolve dynamically, it must approach the chaotic side without slipping over.

Kauffman explicitly states his “order for free” is not thermodynamically free. The order comes at a thermodynamic cost of waste heat in the environment. However, there is something interesting about the network tuning parameters and thermodynamics.

On previous posts I have discussed the progression of the universe from low to high entropy. This is sometimes called the heat death of the universe. At the Big Bang, we had high order and low entropy. At the end of the universe, we will have disorder and high entropy. There seems to be parallel with networks. The Big Bang corresponds to the uninteresting or frozen network pattern and the end of the universe corresponds to the chaotic pattern. The universe appears to be much like a network that is changing its own parameters over time as it operates. The arrow of time is like a sliding set of tuning parameters that is taking the network of the universe from order to disorder.

If Kauffman is right that life operates at the edge of chaos, the fact we are able to exist as living beings must be related to our particular time in the history of universe. In other words, life could not have come about earlier than it did and will not exist in its present form until the end. Consciousness and mind represent the next step up from unconscious life and is built on the paradigm of life and metabolism. Consciousness too could not have come about until just the time the tuning parameters became right for it. The emergence of life and consciousness might come directly from the path from Big Bang to heat death as the natural outgrowth of the network behavior of the universe. Going forward we may find the universe creating ever new forms of complexity and perhaps newer forms of consciousness.

From galaxies to human brains, things appeared to be organized in the same way. Complexity and pattern emerge without predefined plan. We might think of the universe itself as a single network unfolding and evolving itself by its rules. Our brains and minds are small parts of its bigger network and work the same way. Small wonder we should tend to find pattern and meaning in the world where ever we look.

In 1972 Arthur Koestler explored synchronicity and parapsychology in The Roots of Coincidence (6). While investigating whether some a-causal principle could be work in the world, he recounts Carl Jung’s story about treating a woman who was telling a dream she had had about a golden scarab. At that very moment, Jung heard a tapping on the window from an insect. Jung captured the insect and found it to be scarabaeid beetle – the nearest thing found to a scarab in that vicinity. “What causality is ‘up-to’ we think we know quite well: to lend order and stability to the universe which otherwise would be chaotic and unpredictable. Causality means law and order. But what does the scarab at Jung’s window mean?” (7) Koestler asks.

When we think of the world as networks within networks perhaps the causal and the a-causal come from the same place. Networks not only give us complexity and the myriad of forms of this world they also give us “order for free.” The scarab too is part of the greater order just as are many of the other patterns we see.

Koestler almost arrives at this same point when he writes about living organisms and the body social as he describes them as “multi-leveled, hierarchical organized systems of sub-wholes containing sub-wholes of a lower order, like Chinese boxes. These sub-wholes – or ‘holons’, as I have proposed to call them – are Janus faced entities which display both the independent properties of wholes and the dependent properties of parts.” (8)

Chinese boxes are a set of boxes each fitting inside the other. John Fudjack in 1999 used the same Chinese box analogy in attempting to describe consciousness as liminocentrically structured. A liminocentric structure is not precisely fractal but it is fractal-like. You might imagine a recursive set of Chinese boxes where the inner box contains the outer box. If you find that hard to visualize, do a search for M. C. Escher Waterfall to get an idea of how the top and the bottom can somehow join. Although Fudjack’s main focus is on the nested contexts of consciousness, he speculates that “if one is to believe what string theory in physics has to say, extremely large distances in the physical world may be literally identical to (i.e. indistinguishable from) extremely small distances. Physical reality may thus exhibit a fractal identity at its extremities, and turn out to be a liminocentric structure. Liminocentric structures also seem sometimes to manifest strange, paradoxical features – such as holographic organization, in which the part appears to contain the whole.” (9)

The liminocentric vision of the universe unfolding itself like a set of Chinese boxes brings to mind the belief of many traditions in the East that the God without is the God within. I do not generally like to use the term “God” since it carries too many connotations but it would not surprise me to learn that in the inside and on the outside of the Chinese boxes we find some form of a consciousness probably on a level we cannot imagine. Or more simply to quote Carl Sagan :“We long to return. And we can. Because the cosmos is also within us. We’re made of star-stuff. We are a way for the cosmos to know itself.”

Notes

1- Wilhelm, Richard. The I Ching, Princeton University Press, New York, 1950

2- Shermer, Michael. How We Believe. Henry Holt and Company, New York, 2000.

3- Krioukov , Dmitri et al. Network Cosmology.Scientific Reports 2, Article number: 793 November 2012

4- http://techland.time.com/2012/11/28/your-brain-the-internet-and-the-universe-have-something-fascinating-in-common/

5- Kauffman, Stuart. At Home in the Universe: The Search for the Laws of Self-Organization and Complexity. Oxford University Press, Oxford, 1995.

6- Koestler, Arthur. The Roots of Coincidence. Random House, New York, 1972.

7- Ibid p 105.

8- Ibid p 112.

9 – http://tap3x.net/EMBTI/j6structures.html