In his essay Fearful Symmetries, published in the October 2010 issue of the journal First Things, physicist Stephen Barr offered a critique of the modern tendency to make the investigative strategy of reductionism into a “metaphysical prejudice.” It is a mistake, he says, to take the extraordinary success of the scientific practice of looking at things in smaller and simpler parts as proof that “the further we push toward a more basic understanding of things, the more we are immersed in meaningless, brutish bits of matter.”
Perusing the writings of atheistic scientists and philosophers like Daniel Dennett, one could easily get the impression that arriving at a simpler explanation for something equates to a revelation that things are “lower, cruder, and more trivial.” But at the heart of Barr’s critique is the observation that in fundamental physics and advanced mathematics, “simpler” does not mean more chaotic and inchoate, but rather more elegant and beautiful. Those who hold to a philosophical reductionism “overlook the hidden forces and principles” that govern the processes of cosmic evolution.
Barr’s article lays out the way that the work of scientists and mathematicians exploring the fundamental principles of physics (from Kepler to Einstein to those currently running the Large Hadron Collider in Switzerland) actually suggests “that order does not really emerge from chaos, as we might naively assume; it always emerges from greater and more impressive order already present at a deeper level.” This excerpt gives his first example, the starting point from which he guides us into strangely beautiful world of particle physics, and towards the discovery that “matter, although mindless itself, is the product of a Mind of infinite profundity and infinite simplicity.”
“Let’s start with a simple but instructive example of how order can appear to emerge spontaneously from mere chaos through the operation of natural forces. Imagine a large number of identical marbles rolling around randomly in a shoe box. If the box is tilted, all the marbles will roll down into a corner and arrange themselves into what is called the “hexagonal closest packing” pattern. (This is the same pattern one sees in oranges stacked on a fruit stand or in cells in a beehive.) This orderly structure emerges as the result of blind physical forces and mathematical laws. There is no hand arranging it. Physics requires the marbles to lower their gravitational potential energy as much as possible by squeezing down into the corner, which leads to the geometry of hexagonal packing.
At this point it seems as though order has indeed sprung from mere chaos. To see why this is wrong, however, consider a genuinely chaotic situation: a typical teenager’s bedroom. Imagine a huge jack tilting the bedroom so that everything in it slides into a corner. The result would not be an orderly pattern but instead a jumbled heap of lamps, furniture, books, clothing, and what have you.
Why the difference? Part of the answer is that, unlike the objects in the bedroom, the marbles in the box all have the same size and shape. But there’s more to it. Put a number of spoons of the same size and shape into a box and tilt it, and the result will be a jumbled heap. Marbles differ from spoons because their shape is spherical. When spoons tumble into a corner, they end up pointing every which way, but marbles don’t point every which way, because no matter which way a sphere is turned it looks exactly the same.
These two crucial features of the marbles—having the same shape and having a spherical shape—should be understood as principles of order that are already present in the supposedly chaotic situation before the box was tilted. In fact, the more we reduce to deeper explanations, the higher we go. This is because, in a sense that can be made mathematically precise, the preexisting order inherent in the marbles is greater than the order that emerges after the marbles arrange themselves. This requires some explanation.
Both the preexisting order and the order that emerges involve symmetry, a concept of central importance in modern physics, as we’ll see. Mathematicians and physicists have a peculiar way of thinking about symmetry: A symmetry is something that is done. For example, if one rotates a square by 90 degrees, it looks the same, so rotating by 90 degrees is said to be a symmetry of the square. So is rotating by 180 degrees, 270 degrees, or a full 360 degrees. A square thus has exactly four symmetries.
Not surprisingly, the hexagonal pattern the marbles form has six symmetries (rotating by any multiple of 60 degrees: 60, 120, 180, 240, 300, and 360 degrees). A sphere, on the other hand, has an infinite number of symmetries—doubly infinite, in fact, since rotating a sphere by any angle about any axis leaves it looking the same. And, what’s more, the symmetries of a sphere include all the symmetries of a hexagon.
If we think this way about symmetry, careful analysis shows that, when marbles arrange themselves into the hexagonal pattern, just six of the infinite number of symmetries in the shape of the marbles are ex-pressed or manifested in their final arrangement. The rest of the symmetries are said, in the jargon of physics, to be spontaneously broken. So, in the simple example of marbles in a tilted box, we can see that symmetry isn’t popping out of nowhere. It is being distilled out of a greater symmetry already present within the spherical shape of the marbles.”
In the full essay, Barr gives a richer description of how this most basic kind of symmetry is just one sort of order, and how even this form points to other much more complex kinds of symmetry whose properties may be described only through the tools of complex mathematics. As he says, “the symmetries that characterize the deepest laws of physics are mathematically richer and stranger than the ones we encounter in everyday life.” But even more important than the fact that such mathematical concepts exist and are beautiful, more important even than the way such esoteric mathematical symmetries have suggested imminently practical experimental projects, is the way they point to a universe that is anything but brutish and trivial, though its elegance may be hard to see:
“It is true that the cosmos was at one point a swirling mass of gas and dust out of which has come the extraordinary complexity of life as we experience it. Yet, at every moment in this process of development, a greater and more impressive order operates within—an order that did not develop but was there from the beginning. In the upper world, mind, thought, and ideas make their appearance as fruit on the topmost branches of an evolutionary tree. Below the surface, we see the taproots of reality, the fundamental laws of physics that shimmer with ideas of profound simplicity.”