On Wilczek and Symmetry (Inside and Out)

I had the opportunity to attend a talk given by Frank Wilczek, Nobel laureate in physics and author of the book The Lightness of Being.  During the Q and A after the talk he was asked if our aesthetic judgment of symmetry could be said to prejudice scientific inquiry.  Wilczek first pointed to the rich benefits of our search for symmetries.  He then added that he saw our taste for symmetry as a strategy more than a judgment.  I enjoyed the use of the word strategy.  He went on to say that Nature seems to have good taste or that Nature’s taste seems to agree with ours (I’m paraphrasing but I think I got it right).  This choice of words triggered a series of associations, for me, concerning the weave of biology and culture, or of biology and the complex conceptual objects we now perceive.

One of these associations was with something neuroscientist Samir Zeki has said about visual art.  Zeki understands the purpose of vision itself as the acquiring of information about the world.  And he has concluded that since “a search for the constant, lasting, essential and enduring features of objects, surfaces, faces, situations, and so on,” is what allows us to acquire knowledge, it follows that one of the functions of art, (which is often characterized as finding the essential enduring features of a perceived world)  “is an extention of the major function of the visual brain.”   The full paper, Art and the Brain, can be found on the Neuroesthetics Institute web site.

Symmetry is a specific concept or property of objects.  And I found a paper that explores the history of our awareness or use of it.  In The First Appearance of Symmetry in the Human Lineage: Where Perception Meets Art (Derek Hodgson, Department of Archaeology, University of York) the author also refers to work that finds symmetry detection in nonhuman primates.  He tells us, for example, that it has been demonstrated:

that monkeys, raccoons, and birds prefer symmetry to asymmetry and irregularity. This may be related to the fact that symmetry is an enduring aspect of the visual world that has been incorporated into the underlying neural capacities of the brain in terms of capturing the non-accidental properties of the world…..Thus, the preferred response of neurons may have originally derived from the fact that many of the objects that need to be detected are themselves symmetrical….. In addition, most biologically important objects are symmetrical and, in this regard, sensitivity to symmetry may have evolved because it is crucial for discriminating living organisms from inanimate objects. The existence of fractals in natural scenes also reflects the widespread existence of symmetry in nature. Symmetry therefore appears to provide a useful means by which the visual world can be encoded for the purpose of efficient recognition.

Mathematics, of course, brings its own characteristic precision to the definition of symmetry, but it remains tied to fundamental ideas of sameness, balance or regularity.  Wilczek is very clear about the power of mathematical symmetry in one of the chapters of The Lightness of Being called Symmetry Incarnate:

If we know an object has symmetry, we can deduce some of its properties.  If we know a set of objects has symmetry we can infer from our knowledge of one object the existence and properties of others.  And if we know that the laws of the world have symmetry, we can infer from one object the existence, properties, and behavior of new objects…Thus symmetry can be a powerful idea, rich in consequences.  It’s also an idea that Nature is very fond of.

Later in the book, Wilczek also describes physics theories (and their mathematics) as data compression.

The goal is to find the shortest possible message – ideally a single equation – that when unpacked produces a detailed accurate model of the physical world.

This is analogous to what he refers to as the compression of floods of sensory data out of which we construct “small representations of the world adequate to function in it.”  The more compressed, profoundly simple equation we have, the more complex the calculations that unfold them and the “ever richer output that the world turns out to match.”

In general, these observations are telling us that in art, mathematics and science, we seem to be able to elaborate on what the body is built to do, making more (much more) available to the senses. Neural mechanisms that permit our functioning in the world are enhanced, somehow, and recruited to explore the world beyond our immediate needs.  Again, according to Wilczek:

We try to find mathematical structures that mirror reality so completely that no meaningful aspect escapes them….By achieving such a correspondence, we put reality in a form we can manipulate with our minds.

Philosophical realists claim that matter is primary, brains (minds) are made from matter, and concepts emerge from brains.  Idealists claim that concepts are primary, minds are conceptual machines, and conceptual machines create matter.

Finding mathematical structures that mirror reality completely make this two sides of the very same truth, and Wilczek agrees.