Tuesday, June 16, 2020

Does Chaos Emerge from Order, or Order from Chaos?

In his book on the design of the Westminster pavement, Patterns of Thought; the Hidden Meaning of the Great Pavement of Westminster, published in 1991, Richard Foster interprets the meaning of the complex geometric design, which is based on a shape called a quincunx.

PHOTO: https://www.westminster-abbey.org/about-the-abbey/history/cosmati-pavement
A quincunx is a geometric pattern consisting of five points arranged in a cross, with four of them forming a square or rectangle and a fifth at its center. It has its origins in Roman times, and will be most familiar to many of us today as the arrangement of five dots on one of the faces of a six-sided die. It has cropped up in many places as a design principle even, for example, to encourage contemplation in geometrically set-out gardens.

As we can see, the quincunx in the Westminster pavement is actually a series of several interconnected quincunxes in which one can spin outwards, following a line from the center out to the edge, and then return by spiraling inwards. This exit-and-return motif was interpreted by Foster, in this particular arrangement, as a geometrical representation of the creation of the cosmos by God in which all of time and space emanate from and then return to a single principle. That principle is represented by the central circle, which is the largest of the cut stones in the whole floor. In this sense, it encapsulates in broad terms story the created world and salvation history.

This video was made in 2010 after the completion of the restoration of the floor, and prior to its permanent opening to the public, after being hidden under a carpet for 150 years.

As I looked at this, it occurred to me that this geometric portrayal of the connection between the one and the many might give us some clues to the mechanism behind the creation of emergent order.

The existence of patterns of order, such as common law, common sense, and the common good, is discernible when a society as a whole is observed. In these cases, they communicate to us what society as a whole holds to be just, wise, and desirable. Many individuals who might only be dimly aware of their existence, are nevertheless contributing to them by their daily activities and interactions with others, through an innate sense of how these principles apply to them personally. Even those who wish to dissent from the collective order often somehow contribute to it despite themselves. It is not easy for us to eradicate our own human nature.

This pattern of an order which emerges at the macroscopic level out of an array of mathematically random events, events which happen at the level of the individual, and seems to be observable different aspects of existence, is difficult to account for. Rather than clearing up this dilemma of the connection between the one and the many, modern fields of study seem to compound it. In 1974, for example, Frederick Hayek was given a Nobel Prize in economics. One of Hayek’s great insights was the description of what he called the ‘spontaneous order’ of a market that seemed to respond to the collective knowledge of the demand and supply of goods and services, despite the fact that no single person who was participating in the market, including those in government, had full knowledge of this information.

Modern science faces a similar dilemma in its struggle to reconcile quantum physics with Newtonian (or ‘classical’) physics; that is, to explain how the behavior of the individual molecules, atoms, and even the sub-atomic particles from which all matter is composed, gives rise to the order that is observed at the macroscopic level.

In each case, there are no detailed explanations of a mechanism by which the pattern of individual behavior is connected to the pattern of the whole. We simply observe that it is so.

Attempts to provide such a cause will tend to limit attention to the behavior at the level of the individual or particle as a cause of the order at the wider level. So, the assumption is that each system follows what the modern scientist would recognize as the law of cause-and-effect. By this assumption, Newtonian physics is caused by the accumulation of the effects of what happens at the quantum level. By a similar approach, we might argue that what we observe to be common law is caused by the behavior of individuals within that society. But this is an arbitrarily applied restriction that is a handicap to genuine inquiry. In the language of the philosopher, we would say this approach is limiting our consideration to efficient causes only when the explanation might lie elsewhere.

It occurs to me that principle that the interpretation of the pattern of the Westminster pavement outlined above might offer us help here. Perhaps we should consider final causes too?

The central circle in the pattern represents God, who is both the first and final cause of creation. The cosmos comes from God, and it returns to Him. In an isolated system that is a part of the whole, this dynamic would become efficient, proximate, and final causes respectively. Another way of looking at this from a temporal perspective is to say that just as the past pushes, the future pulls. Considered this way, the final cause accommodates efficient causes, just as efficient causes conform to the final.

Under this picture, the emergent order is as much a cause of the individual behavior as it is an effect that arises from it. So we would say that Newton physics could be considered at least as much a cause of quantum events as the other way around, and this being the case, any attempt to explain a mechanism without taking proximate final cause into account would be incomplete. In the social sciences, the ideals of the common good, common law, and even the free market indicate principles of what ought to happen as much as what does (given man’s exercise of free will). So this says that the common good ought to govern the behavior of the person, rather than the other way around.

Culture, the work of man in cultivating the goods and values of nature, is another emergent order. However, in the case of culture, we are accustomed to thinking of it as being simultaneously the cause and effect of human behavior - that is both efficient and proximate final cause. When all of these influences are in harmony with the ultimate final cause then we delight in it and consider it beautiful. We want to live in a beautiful culture because, as Roger Scruton put it, it tells us ‘that we are at home in the world.’

I would go further and say that the recognition of the beauty of these patterns of emergent order, which are based upon what is good and true, will delight us. Consequently, we delight in our apprehension of the beauty of the cosmos, and in a Christian culture. We are delighted because contemplation of them elevates our minds from the particulars to the universals that they point to, and ultimately to God. In the same way, the flawed individuals of the institutional Church direct us collectively to Truth and the mystical body of Christ. God is the uncreated Light that illuminates and delights and whom, ultimately we behold joyfully.

It is our recognition that they direct us to our final rest, maybe only at some pre-conscious level, that causes our delight in details of His creation. Listen to the comments of the people who viewed the pattern of clouds of starlings flying at dawn.

The patterns of the clouds of birds, incidentally, remind me of those of the swirling aurora borealis which are caused by charged particles from the sun striking air molecules in places where the Earth’s magnetic field is strong, that cause those molecules’ atoms to become excited.

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