Richard Bright: Complexity is in us and all around us. Is there a hierarchy of complexity?
Niels Henrik Gregersen: Well, complexity is standardly defined as that which escapes an easy reduction to existing models of rationality. In this sense, complexity is always a framework-dependent concept. What is complex from one perspective may be more simple from another perspective. Some seemingly complex states have turned out to be largely reducible to simple equations, as in mathematical chaos theory. Here the devil lies in the details, that is, in the difficulty of representing the initial conditions with mathematical accuracy.
In the case of algorithmic compressions, the situation is different. The hierarchy between the level of explanation and the level of what is explained here seems to be fully overcome. But even in such cases of “simplexity”, we are not, I think, quite beyond aspects of hierarchy. Algorithmic models usually imply a series of computations based on conditionals, for example: If x applies, do p, but if y applies, rather do q, etc. Such conditionals express a residual hierarchy even in the case of successful algorithms.
Now, if we move from Computational Complexity to Real-World Complexity, I doubt that we can ever understand how nature works without assuming levels at operation in natural networks. Atoms and molecules retain their constituent nature even when brought to function in new complex wholes, say, in cells. This also goes for systems of bigger scope. Gravitational inhomogeneity creates more gravitational clumping leading to star explosions; historically evolved river beds channel the overflow of water running down from mountains and hills; ecosystems host a variety of niches co-created by their elements and organisms. Or take the brain as an example. According to Hebb’s Rule, neurons that fire together wire together. Yet the pre-established wiring also conditions the probability of future firings. Thus, even if the neuronal pathways are made in the process of walking, the walking will still be statistically dependent on the system of pathways carved out prior to the walk. This example seems to me to entail a more general lesson: Even though self-organizational processes may take off from a variety of initial conditions, they never start from scratch.
Finally, as soon as we have cell membranes, a sense of the difference between an inner life world and the external environments emerges. Here a new level of priority emerges, and by implication also a hierarchy of biological wants and values. An individual organism “wants” something from its environment, and something more than something else. Yet also here it seems that such intentional “cravings” presuppose the “carvings” already present in the ecological niches, such as the presence of light, nutrients, or mating options.
RB: Can you give an example (or examples) of how an understanding of complexity advances in the philosophy of religion and our understanding of our place in the world?
Get the Full Experience
Read the rest of this article, and view all articles in full from just £10 for 3 months.