Emergence

It's interesting to see the unexpected connections that you form between your different interests. In response to this post regarding everything happening for a reason, my brother suggested that I look into chaos theory (see Wikipedia along with this excellent brief introduction). In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamic systems that under certain conditions exhibit a phenomenon known as chaos. Among the characteristics of chaotic systems is a sensitivity to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of systems that exhibit chaos appears to be random, even though the system is deterministic in the sense that it is well defined and contains no random parameters. Examples of such systems include the atmosphere, the solar system, plate tectonics, turbulent fluids, economics, and population growth.

The butterfly effect is particularly interesting. The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or, for that matter, prevent a tornado from appearing). The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. On some level, this isn't all that different from my idea that seemingly random things happen in our lives sometimes since they serve some greater purpose (that is unknown to us at the time but has ripple effects within and across people's lives).

In the context of nanotechnology (see this post), this got me thinking about the concept of emergence. Size matters much more with nanotechnology than most other fields since many of the properties that apply at the macroscale do not apply at the nanoscale. Ratner describes cutting a cube of gold into smaller and smaller pieces. He observes that:

“All the gold bricks’ physical and chemical properties will be unchanged. This much is obvious from our real-world experience – at the marcoscale chemical and physical properties of materials are not size dependent. It doesn’t matter whether the cubes are gold, iron, lead, plastic, ice, or brass. When we reach the nanoscale, though, everything will change, including the gold’s color, melting point, and chemical properties. The reason for this change has to do with the nature of the interactions among the atoms that make up the gold, interactions that are averaged out of existence in the bulk material. Nano gold doesn’t act like bulk gold.”

Ratner further points out that the “coupling of size with the most fundamental chemical, electrical and physical properties of materials is key to all nanoscience.” With the Big Bang, particles of energy and atoms were created with certain properties that govern all larger building blocks and processes of life on Earth. Atoms combine to form molecules, molecules combine to form molecular networks, and so on up to the planet’s ecosystem. With each new level of atomic construction, new properties and interactions emerge that did not exist at the previous level (but are governed by the properties of the preceding levels). One way to think about this is as a complex system – specifically “a system whose properties are not fully explained by an understanding of its component parts. Complex systems consist of a large number of mutually interacting and interwoven parts, entities or agents.” In response to the complexity of the interactions that take place at each level of nature, various (layered) disciplines have emerged: math as operating system of the universe, physics as the universe in motion, chemistry as physics in motion, biology as molecular networks, and ecology as interconnected networks.

Within this context, one interesting concept is scale-free networks. According the Wikipedia, “a scale-free network is a specific kind of complex network [in which] some nodes act as ‘highly connected hubs’ (high degree), although most nodes are of low degree.” One important property of scale-free network is that they are self-similar – meaning each part of the network is “exactly or approximately similar to a part of itself”. One example of a self-similar structure is a fractal. As the Wikipedia says, “in colloquial usage, [a fractal] denotes a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification and is therefore often referred to as ‘infinitely complex.’” Many objects within nature including clouds, snowflakes, mountains, river networks, and systems of blood vessels have been shown to be fractal in nature. (Sound familiar? Fractals are also important in chaos theory!)

This is not surprising, however, given that all of these macrostructures are built up of atoms. In studying the connectedness of the Web, physicist Albert-Laszlo Barabasi and his colleagues at the University of Notre Dame “found that the probability p(k) that a node in the network connects with k other nodes was, in a given network, proportional to k^−γ. The degree exponent γ is not universal and depends on the detail of network structure. Numerical values of the exponent γ for various systems are diverse but most of them are in the range 2 < γ ≤ 3.” Within the world of atoms, the maximum electrons in the nth shell is computed as 2n^2. Atomic valence dictates possible chemical reactions, chemical reactions drive biological functions, and so on. Nature becomes an “infinitely complex” system that “appears similar at all scales of magnification” and is ultimately governed by fundamental properties at the atomic and subatomic level. (Note: The connection between atomic valence and the properties of scale-free networks is potentially a stretch on my part but an interesting one in my opinion) Many people think science and mathematics are at odds with religion. They think science and math make God irrelevant. I actually think they could be helpful in terms of understanding how God operates and interacts with us in our daily lives. When you look at how nature operates and how elegant mathematics is, it's hard for me to believe that God doesn't have a hand in it. It's just all too perfect to be that way by chance (or even things like natural selection). Bringing all this together, two interesting questions to think about are: (1) If different properties emerge as you put more and more atoms together, what properties emerge as you put more and more people together? How are these properties influenced through a combination of God's will/plan and human free will? and (2) Even though life seems random and chaotic, could it really be "deterministic in the sense that it is well defined and contains no random parameters"? Can chaos theory help us better understand the nature of God's relationship with man?