The title is taken from the titles of two books: “Complexification” by John L. Casti, and “The Mind of God” by Paul Davies.
The chapters in “Complexification” are entitled: The Simple and the Complex, The Catastrophic, The Chaotic, The Lawless, The Irreducible, The Emergent, and The Simply Complex. I skimmed the table of contents while standing up in a big Toronto bookstore, and didn’t have the time even to skim the chapters, let alone read the book. Some day I hope to go back to it. But in the meantime, I want to speculate on these chapter headings.
To me, “the catastrophic” means the discontinuous, as in the jump from a higher to a lower level (or vice versa) in a cup Catastrophe, or the quantum jump of an electron from a lower to a higher energy level within an atom. “The chaotic” means the strange, as in “strange attractor”; the super-sensitive non-linear dynamic instability of systems which are unpredictable, though deterministic. “The lawless” means the truly objectively random, if there is such a thing, as in the presumed unpredictability of when a radioactive atom will emit an alpha or a beta particle, and thereby possibly kill the Schrodinger cat. “The irreducible” means a system that is not decomposable because of its high inter-connectivity — a system that is not simply the sum of its parts. “The emergent” means that new properties (like life and mind) have emerged from the irreducible inter-connectivity of a system.
These are indeed the five characteristics by which the complex system differs from the simple system, which would be continuous, linear, predictable, decomposable, and only the sum of its parts. We have here the rudiments of the science of the complex, needed to complement the science of the very small (quantum mechanics), the science of the very large or very fast (relativity theory), and the science of the very numerous (thermodynamics and statistical mechanics).
In Davies’ book “The Mind of God”, which I barely had time to leaf through standing in the same bookstore, he defines two terms, “algorithmic complexity” and “logical depth”, which I find helpful. Algorithmic complexity is the length of the minimal program that would yield the observed output in a computer simulation. For example, if the output is to be a repeating wallpaper design, the program would only have to specify the unit cell and then say “repeat” in two dimensions. That would be a simple system. But if the system is a real rose garden, that would not be possible; yet a rose garden is not a random jumble, but highly ordered in a different sense from the wallpaper pattern. A living cell has a different type of order from a perfect crystal, yet both are far away from a random jumble. The difference between a cell and a crystal is due to the much greater algorithmic complexity of the cell. Living systems are generally not “algorithmically compressible”, i.e. the program would take almost as long to specify as the system itself. In such cases simulation is useless; observation of reality is the only way to gain insightful knowledge. Perhaps this is why God had to create the world, because a mere “thought experiment” could not give Him the required knowledge. This assumes that even God does not know how the reality experiment will end – i.e. He is not all-knowing or all-powerful.
The other concept in Davies’ book is “logical depth”, defined as the running time for the minimal program to generate the observed output. Again, simple patterns are logically shallow, complex patterns are logically deep. It took life billions of years to run the program and it is still running. Will it ever halt at some Teilhardian Omega point? (It could of course be interrupted or aborted, like pulling the plug on the computer.)
Logically deep systems are recognized intuitively because we value them and try to preserve them — they would be so difficult to re-create: paintings, scientific theories, works of music or literature are valued far more than shallower objects such as cars, salt crystals, or tin cans.
Yet the two concepts, algorithmic complexity and logical depth are different, the first having to do with the length of the minimal program to reproduce the system, the second with the running time of this minimal program to reproduce the system. A Koch snowflake has very low algorithmic complexity — a child could describe how to generate it; but it is logically so deep that the program never halts — it runs for infinity.